Jean de Climont












Editions d'Assailly









































ISBN 978 2 9024 2524 2

© Editions d'Assailly, 2014, 2016








The implementation of the kinetic momentum theorem to the friction within fluids




Physical modelling of volume waves within free surface liquids




Swell physical modelling




Ocean Tides




Implementation of the Hamilton’s principle in fluid mechanics




Polarization of the K coronal layer of the Sun within the Galaxy plane




The consequences of Pr. Allais' second option of his third hypothesis to explain the results of his analysis of Miller's interferometer measurements




The inversion of the electron magnetic property and its implication.




Gravitation zonal effects.




Electron beams magnetic field




Electron intrinsic magnetic field is not a dipole, the Rowland effect.









The implementation

of the kinetic momentum theorem

to the friction

within fluids



A common solution to both fluid mechanics



swelling of the surface of whirl-well flows


laminar separation point

of the flow around a cylinder



of the flow

around a cylinder










March 1995






The free surface of whirl-well flows is above the theoretical level.


The azimutal angle of separation of the laminar flow around a cylinder is about 82°. Neither the speed profiles, nor the various asumptions proposed up to now, allow for such an angle below 90° which is the angle where the differential pressure sign changes.


Using the kinetic momentum theorem, the Fluid Mechanics equations in cylindrical coordinates have been directly established. They provide a complementary term related to the Coriolis acceleration. However, they mainly allow for a new approach of friction within fluids, leading to a common solution to both non conformances, complying with experiments. In addition, a full and accurate description of the various configurations of the flow around a cylinder has been obtained. 






01 Objectives

02 Principles




11 Cylindrical coordinate equations

12 Analysis of the complementary term

13. Moments of the friction forces

14. New expression of frictions




21 Relative speeds within the fluid

22 Modified equations

23 Boundary conditions

24 Results

25 Friction effect on the bottom 

26 Lowering of the air pressure as a result of the sweeping by the vortex




31 Relative speeds within the fluid

32 Modified equations

33 Boundary conditions

34 Results: the flow configurations

35 Equation of the boundary layer

36 Results: the separation points



41 Relative speeds within the fluid

42 Equation of the parietal sheet

43 Equation within the fluid

44 Results




51 Equations of the whirl-well flow (CODES PTAVEVO, PTSANVO et PTFRORA.BAS)

52 Equations of the flow around a cylinder (CODE CYLINDRE.BAS,CYCLTU1.BAS)

53 Equations of the superfluid helium    (CODE HELIUM.BAS)

54 Polhausen and modified Polhausen methods(CODES POLHA50,LAMNNAP et LAM1NAP.BAS)





01 Objectives


During the last two decades, the visco and plasto-elastic models allow for major improvements in the knowledge of material behaviour. In the meantime, fluid mechanics remains fully experimental. There is still a large gap between theoretical solutions and experimental results.


At the beginning of the twentieth century, Fluids mechanics was considered by high level scientists as a lumpen-science. No improvements of the modelling have been proposed which could be compared to those implemented in various technical areas. Conversely, huge investments and increasing testing expenses are made in order to balance a lack of knowledge hidden by subtle calculations. Unexpected vibrations, unforeseen separations, untimely cavitations and overflows occurring at random are still the dread of engineers.


Two other kinds of difficulties are prevailing in the present approach of friction within viscous fluid flows.


These flows are always producing vortices. When the flow is symmetrical, two opposite vortices are generated. Thus, it seems that the flow is complying with the kinetic moment conservation principle. It is not. Half a cylinder lying on a plane generates only one line of vortex, fully developed, although the flow is disturbed by the plane. Furthermore, such a global approach of the kinetic moment conservation principle hides the time factor. The wake vortices cannot appear just when the flow passes the edge. The kinetic moment shall already be in the fluid before. Even less could they be their own reciprocal cause of existence.


The second kind of difficulties is related to the accumulation of energy within the boundary layer. The part of this energy not dissipated within the boundary layer, is dissipated within the wake, but the form under which this energy is accumulated is not identified. Even so, this energy is not taken into account. The eddy form shown by the wake surely gives the solution.


This report is devoted to the kinetic friction within fluids. The word "kinetic" is used there as usual, although not fully logic" to designate the phenomena related to the moments in the frame of the kinetic moment theorem as opposed to the dynamic effects studied in the frame of the momentum theorem


02 Principles


The mass conservation equation is not changed.


Only permanent and incompressible plane flows are envisaged.


The moments only exist for rotating flows, or part of flows. Thus only one equation is involved. The other ones are obtained by projection of the inertia and forces on the axis of the plane rotating flow and on the direction of the origin within the plane.


The applicable equations have been established in each case, nevertheless, the inertial moment and pressure effect moment are common to all cases; they have been set up in the next paragraph.






11 Cylindrical coordinate equations


The kinetic momentum theorem applied to the projections on the fluid trickle tangent writes for a volume element:



Where I is the moment of inertia of the volume element related to the axis of the cylindrical coordinate perpendicular to the flow plane. is the local angular speed of the flow.


i is the moment of inertia of the fluid components related to an axis perpendicular to the flow plane and including their gravity centre and the angular speed of those elements around this axis. The product of the moment of inertia and of the angular velocities shall be summed up within the volume element.


Within the former dynamic approach of friction, the moments of the friction forces are related both to the flow axis and to each of the volume elements' axis. The terms of the equation related to friction in the former approach are easy to be retrieved and they write:



The first term of the second member of this equation is the moment of the variation of t related to the distance, the second is the couple resulting from t on each face involved of the volume element and the third term is the deduction of the sold body rotation not involving any relative movement.


The main moment of inertia may be written in a more usual way:



Then it may be written



12 Analysis of the complementary term


The equation includes a complementary term not found when it is directly derives from the Cartesian coordinates equation. However this term is always negligible against the others as far as the angular speed of the fluid components, should they be Helmoltz tubes or spinning particles made of a limited amount of molecules, is only a result of a general rotating motion of the fluid around the origin of coordinates. Nevertheless, when this motion is very slow, and of course when there is no motion, this term related to the own moment of inertia of the fluid particles may have major effects. In addition it may take non negligible values when the fluid volume involved is great enough. This is the case for large Helmoltz tube. In this case the motion of such tubes may be determined within a rotating fluid. This term is not new. It is equivalent to what is called the CORIOLIS acceleration for the motion of a massive point in the pure mechanical point of view. The result in fluid is a term equivalent to a pressure, which could be named CORIOLIS pressure.


However, this term has no impact on the results of this report. Of course high moments of inertia may be found within the two flows studied by this report. They are located where the radius of curvature is very small, mainly near the edge of the hole for the whirl-well flow and at the leading point for the flow around a cylinder. Nevertheless, the radius of curvature has no effect on particles when their dimension is greater than this radius. It is not consistent to reduce the integration step below this dimension aiming at an increase of the moment of inertia. Even though this would be done, the effect of such a moment of inertia will not allow for explaining by the same way both non conformances subject of this report, mainly because the areas where such an event could occur are not in line between both flows, and not in line within each flow with the areas where the non conformances occur.


13 Moments of friction forces


In most case, the inertia moment of fluid particles may be neglected. However, as soon as it is considered that those particles may turn around themselves, there is friction between them. The rotation of the fluid particles around themselves creates friction not existing otherwise. Moreover if such a rotation is produced within flows deriving from a potential as it is the case for all flows within this report, kinetic friction appears although the old approach of friction did not allow for any friction.


This report is based upon this assumption that a gradient of speed within a flow makes the fluid particles rotating around themselves. Thus the friction terms of the viscous fluid mechanics equations are dramatically changed.


It shall be noted that quantitative results are only given in this report where the phenomena are independent from the dimension of the fluid particles. The notion of "fluid particle" remains undefined as previously. There are experimental results that may need the knowledge of this dimension in order to enable explaining what happens, but this is the purpose of a future report.


The rationale is to determine the kinetic friction parameter values for the whirl-well flow both with vortex and without vortex, then to validate the new approach by implementing these values of the parameters to the flow around a cylinder. The validation appears not to be possible only for very small Reynolds numbers (below 10, i.e. without any industrial impact) by lack of experimental data.


As impressive as is the compliance with the well-known experimental results, a coincidence cannot be eliminated. Thus the new approach has been applied to the motion of superfluid helium in a rotating bucket. Again most of the well-known experimental results are explained, nevertheless only the approach is validated in this case for the value of the kinetic friction parameters are not the same as those in water.


Note related to the kinetic moment of the fluid particles.

It could be thought that such a moment is internal and should not be taken into account and the kinetic friction as well should not be considered to study the overall motion of fluids. This is of course fully wrong. This would not be in line with the kinetic moment conservation principle. The easiest way to be convinced is to consider the rotation of a gyroscope. The overall kinetic moment depends mainly on the kinetic moment of the fly wheel inside. The same applies to the fluid particles.


14. New expression of friction


The kinetic friction acts through their moments. The tangential friction, parallel to the fluid flow, maintains the rotation of the fluid particles around themselves. This rotation generates a radial friction between fluid particles as shown by the following sketch.





The index f is related to the friction within the fluid. Indices t and r are related to the tangential and radial direction with regard to the local speed of flow although friction between fluid particles is always tangential. Along the walls, f is replaced by p (as parietal). There is no reason to believe that the friction parameters have the same value between particles themselves and between particles and walls. This is by the way a mean to take into account the wall roughness. Nevertheless within this report, it is always considered that the roughness is very small so that the walls are covered with a fine layer of motionless fluid, like painted, so that friction occurs every where between fluid particles only.


The kinetic friction may be related to either Helmoltz tubes or fluid particles relative rotation. This friction is proportional to the surface of these tubes or particles in contact. These surfaces are either part of cylinders or part of spheres; their radius is designated as af.


The kinetic friction coefficient is designated as the kinetic viscosity kf (dimension ML-1T-1). The definition of this coefficient is similar to the definition of the dynamic viscosity. It is assumed that the speed of rotation of either the tubes or the particles, is proportional to the difference between their speed within the fluid. Thus the friction moments are balanced within permanent flows independently from the speed of the flows.


The ratio of the angular speed to the speed gradient is designated as kkf. This is an adimensional slipping coefficient of tubes or particles between them.

The friction strengths are proportional to the relative peripheral speeds of tubes and particles and to the inverse of the contact surface da:




Moreover, the solid body rotation does not imply any relative motion so that the related speed difference shall be corrected accordingly.


It shall be noted that fluid nooks are left by the Helmoltz tubes and the fluid particles gathered within layers or sheets. These fluid nooks are subjected to friction and shear stresses. The moments related to these effects have not been taken into account. Thus they are implicitly introduced into the kinetic coefficient values obtained from the experimental results related to the whirl-well flows. As far as the speed gradients have the same sign and same order of magnitude in both the whirl-well flow and the flow around a cylinder, it may be considered that the effect of nooks is similar for both flows. Any way, the results obtained for the flow around a cylinder are complying with experiments when these values of the kinetic parameters are used. This is no more the case for very high Reynolds numbers, although the critical values are not changed. In such high speed conditions, those fluid nooks have a major consequence. They allow for explaining the most remarkable phenomenon of the fluid mechanics: the transition between laminar and turbulent flows.




The solid body rotation


15. Dynamic viscosity, kinetic viscosity and slipping


The kinetic friction


Along an indefinite plane, the kinetic viscosity may be calculated from the dynamic viscosity and the slipping coefficient. The shear stress is the same in both cases as the curvature radius is infinite. The only resulting shear stress is tangential. The shear stress writes in each case:


The shear stresses of the dynamic and kinetic friction approaches are respectively:





When the order of magnitude of the last term is small against kkf, it may be written:




In the other flows, there is always a curvature. Thus it is necessary to write the full equations. Nevertheless it happens that the slipping coefficient is always linked to the radius of the tubes or fluid particles for both the whirl-well flow and the flow around a cylinder. The related terms may be neglected. The opposite situation occurs in the motion of superfluid helium in a rotating bucket, and this is the reason why only qualitative results are drawn in that case.


In order to make equation easier to be written, the slipping coefficient is always positive and takes values between 1 (no slipping) and 0 (no rotation). It should have been more consistent to define an algebraic coefficient (-1,+1), but the need to write the equations in each case when using a positive coefficient only was considered as a good way to check several times the correctness of the equations. At the end, an algebraic coefficient was used for helium motion.


All the equations and most of the calculation codes have been written taking into account all terms including the slipping coefficient. Its effect has been checked and does not affect the results provided the radius af remains small enough (say below 1mm) excepted of course for the motion of helium.




21 Relative speeds within the fluid


The conventional cylindrical coordinates are used together with the notation defined above for friction. The friction on the bottom is calculated in § 25. Only the friction within the fluid is first considered. It shall be reminded that the whirl-well flow is a typical irrotational flow deriving from a potential, so that there is no friction in the old approach. It is not the same within the new approach as shown hereafter.


21.1 Tangential relative speed:






21.2 Radial  relative speed:




22 Modified equations


a) Moments:

            1. tangential volume friction     

            2. radial volume friction           


b) Summation within the fluid volume element dx dy dz



c) Division by r r dx dy dz and replacement of strength by their value:



d) Replacement of the speed variations by their value:



The equation of §11 becomes, in the frame of the whirl-well flow:





23 Boundary conditions


23.1 Whirl-well flow with vortex


The only results available are those related to the experiments performed by professor OSTUBO, as reported by the "Traité d'Hydraulique Générale" of professor ESCANDE. The case where the load is Zinfinite=0.207m with a 0.02m opening, has been chosen. The flow rate has been calculated taking into account a flow rate coefficient of 1 applied to the surface included between the edge of the hole and the vertical cylindrical surface of the flow in the hole. This coefficient had been chosen in line with the bell-shaped downstream flow after the hole. The most probable radial speed has been calculated accordingly. The tangential speed has been calculated so that the theoretical surface coincides with the calculated water surface, when the kinetic friction is not taken into account. At a distance designated as Rinf = 0.1m where calculations begin, the tangential and radial speeds are respectively: V0=0.004866m/s and U0=-V0/9.0524.


It shall be noticed that the mathematical model used takes into account the radial speed and the surface lowering speed to calculate the level of the water surface. Thus the lowering of the water free surface is beyond the value obtained in the basic whirl-well flow as presented in the literature. As a result the swelling of the free surface shall be larger than expected when those speeds are not taken into account. The free surface lowering excess results mainly from the radial speed.


23.2 Whirl-well flow without vortex


Here again a curve given by the "Traité d'Hydraulique Générale" has been used. It is a curve giving the tangential speed with regard to the distance to the axis of the hole. The speeds have been calculated so that the theoretical curve coincides with the calculated curve when the kinetic friction is not taken into account. These speeds are as follows: V0=0.0014m/s and U0=-V0/9.0524 the other boundary conditions being the same as for the vortex case.


The theoretical flow mathematical model is stable by itself, provided the boundary conditions are precisely entered as far as possible from the hole. Corrections have been developed first to improve the secant method results. They were found very efficient for polynomial solutions with powers included in the range -5 to +5. Although they were installed in the codes, they are inhibited to reduce the calculation duration, already very long even with computer processor 80486, 33Mhz. The gap with theoretical results remains within the width of the curve line for the lower speeds.  


23.3 Hole


Improvement of the results has been tested by fixing objectives downstream conditions after the hole. Although many iterations were performed, it had not been possible to obtain acceptable results. During these tests it had been noticed that the free surface was not affected by the downstream conditions.



Both experimental curves of the "Traité d'Hydraulique Générale" have been scanerized and printed thereunder.





24 Results


It is not feasible to retrieve the tangential speed curve of the whirl-well flow without vortex when only one value of the kinetic viscosity is chosen. The hypothesis is made that the kinetic viscosity is very small for speed gradients lower than 2s-1. The ratio of kinetic viscosity to the water mass

per volume unit enabling a good compliance of both the experimental curve and the calculate one is kf/r= 0.5*10-6 m2s-1 up to a 2s-1 gradient. Beyond this value the fall is very sharp whatever is the kinetic viscosity above kf/r=10-5m2s-1. It shall be noticed that the true critical gradient is 4s-1 when the solid body rotation is taken into account to evaluate the speed variation inducing the rotation of the fluid particles or tubes.


This first critical gradient was used to determine the value of kf/r allowing for the best compliance between the experimental results obtained by professor OSTUBO and the whirl-well flow water surface calculated when the kinetic friction is taken into account. The most suitable value is kf/r=1.5*10-4 m2s-1.


This value allows for compensating not only the discrepancy between the theoretical basic flow and the experimental result, but also the additional fall of the surface due to the radial speed being verticalized by the hole. It seems that the tangential speed is not verticalized as it causes the bell-shaped flow of the downstream flow.


It could be noticed that a swelling of the free surface complying with the experimental value at the hole level, is achievable with a kinetic viscosity 15 times less than the above value, but without critical gradient. Nevertheless, the coincidence is only obtained at the top part of the curve which deviate from the experimental curve for higher distance. In fact this value of the kinetic viscosity leads to a straight line with a slope smaller than the curve. Such a result cannot be considered as acceptable so that the hypothesis of the existence of two values of the kinetic viscosity can be considered as consistent with the experimental results.


It could be thought that first HELMOLTZ tubes are generated. When the speed gradient increases, they are cut to form fluid particles made of a large number of molecules.


The curves obtained from the calculation have been printed close to the experimental curves.



25 Friction effect on the bottom 


It could be thought that as the friction causes a swelling of the free surface, the same applies to the friction on the bottom. This is wrong, for the signs of the related moments are not the same. The kinetic friction moments act in the same way as the fluid motion which is accelerated towards the axis although the bottom friction moment acts in the opposite way. Notwithstanding this fact, the effect of the friction on the bottom has been calculated. The value obtained is so tiny that it is included in the curve line width.


The calculation was done according to the old friction approach with a Reynolds number as great as 4200. Then one obtains:





26 Lowering of the air pressure as a result of the sweeping by the vortex


Conversely, the effect of the air sweeping by the flow in the vortex of the whirl-well flow has the same direction as the kinetic friction. Thus it induces also a swelling of the free surface.


The most extreme conditions have been taken to favour the air effect. All the air includes in the vortex is considered as swept by the water and with the same speed. The vertical water speed responsible for the air sweeping is taken as large as the full radial speed thus considered as fully verticalized. In addition the sweeping is calculated on the full height of the water between the surface level far away and the bottom.





Definitely this is not enough. The value obtained from this extreme hypothesis remains far below 4 orders of magnitude compared with the experimental results.




31 Relative speeds within the fluid


31.1 Tangential relative speed


As far as the curvature is the main topic of this new friction approach, conventional notations for cylindrical coordinates are also used in this part. Nevertheless, the study of the boundary layer is made using the Cartesian coordinates, as usual in that case, while the curvature will not be neglected. This lack of consistency presents the advantage of allowing for an easy verification of the equations obtained in the related part of this chapter against the large amount of literature related to the boundary layer.


The equations are the same as those obtained in §§ 21.1 and 21.2, as the tangential speed signs are the same.



31.2 Radial relative speed




or by approximation




The calculation uses the tangential speed of the theoretical irrotational flow around a cylinder for integration stability purpose (see chapter 50).





32 Modified equations


The equation of the motion within the fluid writes:




The code CYLINDRE.BAS allows for calculating the tangential speed as modified when taking into account the kinetic friction (reservations are explained in chapter 50 CODING)


It shall be noticed that only the tangential speed gradient and only the moment with regard to the axis of the cylinder have been considered although there are other speed gradients and thus other kinetic strength moments in this kind of flow. This is mainly the case at the leading point. However the calculation is in that case rather intricate although a code was developed to calculate the effect of the moments of inertia, and delivers both the radius and the curvature centre position evolving along the flow. Some improvements remain to be done.


33 Boundary conditions


The calculations have been performed for a 0.04m cylinder radius in water. The boundary conditions are those of the theoretical flow at a distance of 100 times the step. In most cases the step is as small as 0.001m, but in some unstable cases it has been decreased to 0.0001m and sometimes even below.


No assumption was made about the wall speed in this part. This is not the case within the part hereafter devoted to the study of the boundary layer, leading to the precise separation point calculation. No friction is first assumed on the wall.


The calculations deliver the tangential and radial speeds as well as the pressure for each step.


34 Results: the flow configurations


The flow around a cylinder with a given radius is characterised by a sequence of stable states fully differentiated obtained when the speed is increased. These states are reminded in the table thereafter. They refer to the Reynolds number as usual.
























de 50 à 5000








from 5000 to 2/300 000

(separation azimuth 82°)










above 2 to 300 000

(separation azimuth 120°)



The main characteristic of the equation of the § 32 is that the remote speed module is implicitly present in each of its terms. The kinetic friction effect has thus a relative effect decreasing when the speed is increasing. Thus the flow should reach a separation point before an azimuth of 90° for very low Reynolds numbers (1 to 10) if the first kinetic viscosity kf1=0.5m2s-1 obtained from the whirl-well flow was acting from the lowest speed. As it is not the case, this first lower kinetic viscosity shall be also subject to a first critical speed gradient. That is to say that the rotation of fluid tubes or particles is not possible when the tangential speed gradient remains below a minimum value. This value cannot be determined by the whirl-well flow without vortex because the friction is too low to be seen on the experimental curve. This first critical gradient should be below 1.5*10-2s-1; this is the value used for the calculation.


In these conditions, flows around a cylinder with Reynolds numbers below 50 do not involve kinetic friction with the exception of the boundary layer where the gradient is higher as explained in the related part of this report. Friction shall be considered in the former dynamic point of view.


From a speed of 0.0006m/s, thus for a Reynolds number of 50, the tangential speed gradient reaches the first critical value 1.5*10-2s-1. Above that speed a sharp fall of the tangential speed occurs for an azimuth close to 85°.



For Re=50 the theoretical and calculated curves are identical., but for Re= 2000, the fall is fully characterised.


The second critical gradient (2s-1as determined by the whirl-well flow with vortex) is reached only for a tangential speed of 0.626m/s with Re=5000. The kinetic viscosity is then kf/r=1.5*10-4 m2s-1 where the gradient is above the critical value. The fall occurs at an azimuth of about 80°.


For Reynolds numbers in the range of 5000 to about 300 000 the lower viscosity effect disappears so that the fall occurs near 82°. The relative effect of the second value of the kinetic friction decrease slowly and finally disappears completely above Re=6 to 800 000.



In the mean time, the kinetic friction is responsible for another phenomenon above Re=200 000. The peripheral tangential speed of the rotating water particles belonging to two adjacent sheets resulting from the slipping, increases in the meantime and the gradient related to their distance reaches the second critical gradient.


This gradient is approximately 4*V0*(1-kkf)/r. The critical gradient is 4 s-1 when the solid body rotation is taken into account. With (1-kkf) equal to the value obtained from §21 when  kf=150m the related Reynolds number is then 240 000, provided the approximation made are acceptable.


For such a gradient value, new rotating particles should take form, and the most probable is that they take form from the water nooks between the existing rotating particles. As many bolts as nooks take form, locking the sheeted structure of the laminar flow. However as the flow shall continue under the effect of the friction of the remote sheets, the structure is destroyed although the gradients still exist and maintain the rotation of the fluid particles now distributed at random.


It shall be added there that the Reynolds number set values for the transition between the flow configurations have been determined for a given radius of the cylinder. As the gradient does not vary as the Reynolds number, it is evident that the set values are change when the radius is changed. This could explain a part of the large discrepancies between the experimental results.









Although the separation point can only be determined by the detail study of the boundary layer, it appears that the configurations of the flow around a cylinder are mainly determined by the kinetic friction which modify deeply the flow itself.


Moreover the kinetic friction allows for an interpretation of the transition between laminar and turbulent flows.


























configuration and

Reynolds number












separation azimuth, flow within the fluid, speed profile within the boundary layer, method and remarks

1 à 10





variable, perfect fluid, Polhausen, separation non calculated, very thick boundary layer!







90°, perfect fluid, Polhausen modified, all layers affected by the lower kinetic friction viscosity, conforming calculated separation.







90°, perfect fluid, Polhausen modified, wall layer  affected by the higher kinetic friction viscosity, conforming calculated separation


"Karman street"





90°, Equation within the fluid modified by the lower kinetic friction viscosity, Polhausen modified, all layers affected by the higher kinetic friction viscosity, wake vortices explained, conforming calculated separation.









82°, Equation within the fluid modified by the higher kinetic friction viscosity,  Polhausen modified, all layers affected by the higher kinetic friction viscosity, conforming calculated separation.


200 000








120°, higher kinetic friction viscosity without influence on the speed curve, destruction of sheeted laminar structuree, speed profild to the n<1, higher kinetic friction viscosity, without influence except in the boundary layer parietal layer, calculated separation depending on n, conforming for n=0.2









35 Boundary layer equation


35.1 relative speeds within the boundary layer and within the fluid tubes or particles wall layer


35.1.1 Within the fluid of the boundary layer

a) Tangential relative speed:

The effect of the solid body rotation is neglected



b) Radial relative speed




35.1.2 Wall/wall layer hypothesis

The speed gradient within the boundary layer is large enough to allow in all cases a wall layer of tubes or fluid particles to be formed. The equations are the same in both cases. Only the fluid element's radius is changed. The radius of those elements is written ap. These radii ap and af have no reason to be constant. Certainly they are changing along the wall; they are probably increasing with the wall gradient. Nevertheless taking into account such an evolution leads to rather intricate calculations. Even more, the solving of the differential equations is fully unstable when such evolution is taken into account when it has been neglected during the derivation process. It has been checked in some stable enough cases that the separation azimuth seems not to be increased by an evolution of these radii.

a) Tangential relative speed:



b) Radial relative speed




35.1.3 Fluid/wall layer hypothesis



35.2 Wall layer equation


35.2.1 General equation

The inertia forces being negligible close to the wall, the friction force moments are approximately balancing the pressure force moment on the volume element dx dy dz. The situation is exactly identical to the Prandtl's hypothesis.




35.2.2 Friction moments' calculation (first term of §11 equation):

a) Friction force moments:

            1. tangential friction                 

            2. radial friction                                  

            3. Wall/fluid particles friction



b) Summation in space dx *2ap:






c) Value of t strengths:

Generally speaking, t strengths are proportional to the relative speed and to the inverse of the contact surface da. The friction coefficient is the kinetic viscosity kp .




d) Replacing t by their value:





e) Replacing ds by dzda:






f) Division by 2aprR0dxdz:





g) ap and af are very small against R0; the §22.1 expression becomes:



h) Replacing Du par their value:


i) ap/R0 terms may be neglected:


           (35.2.2 i)


35.3 Global boundary layer equation


a) Moments:

            1. tangential volume friction     

            2. radial volume friction           


            3. Wall/fluid particles radial and tangential friction



          3. Wall/fluid particles radial and tangential friction

b) Summation in space dx dy and integration from 0 up to   :






c) Replacing t by their value:






d) Simplifications







e) Replacing Du par their value:






f) Integration processing and division by rR0dxdz:






g) Replacement by boundary values






h) Gathering u and subsequent derivative terms:



i) ap/R0 terms may be neglected:



j) Gathering u and up terms:


k) Deleting terms very small against those including R0/ap:




35.4 Boundary layer speed profile:

As it has been assumed that the tubes or fluid particles are rotating, the speed up of the wall layer is not null. The POLHAUSEN polynomial form becomes:


then:                                        A+B+C+D = 1

                                               B+2C+3D  = 0

                                                     2C+6D = 0


thus :  B=-C,    D=-C/3    and    A=1+C/3.

Replacing up, du/dy and d2u/dy2 by they value, the expression 35.2.2.i becomes:


then one obtains:

35.5 Boundary layer thicknesses and subsequent derivatives


35.5.1 Thicknesses


It is then possible to evaluate d1 (displacement thickness) and d2 (momentum thickness), as function of L, e and g:



35.5.2 Thicknesses' derivatives

The Karman relation involves the derivatives of d and d2 :



Bringing the second relation within the first one obtains:



From now the expression d2/d is designated as FF.


35.5.3 dFF/dx calculation from § 35.5.1:



that can be written:




35.5.4 dC/dx calculation from 35.5.1:




that can be written:





35.6 Karman relation:



Carrying the second term in the §35.3k expression it comes:



that can be written:



as the second term does not included dL/dx, one can write:




replacing the thicknesses and their successive derivatives by their value within 35.5.2:


reminding 35.5.2:                    









finally, replacing dC/dx by its value, one obtains:






35.6 Reynolds numbers higher than 200 000 (turbulent flows):


The POLHAUSEN polynomial profile is no more suitable. Moreover the existence of a wall layer made of rotating particles allows for not taking into account the former assumption of a null fluid speed derivative on the wall surface to obtain the separation point. The separation condition is more simply now the collapse of the wall layer speed. Thus the KARMAN-POLHAUSEN method may be used in turbulent flows when the polynomial profile is replaced by the following one:



with n = 0.1 to 0.2.


This kind of profile is tangent to the theoretical profile only for very thick boundary layer. Thus the tangent boundary condition is replaced by making equal the upper part boundary layer speed to the theoretical speed.



The separation occurs after L is null that is to say after 90°.




When only the wall layer is considered, one obtains:




36 Results: the separation points


Note: the synthesis of the results is given page 28 together with the configurations of the flow around a cylinder.


36.1 Very low Reynolds numbers (1 <e < 10)


The tangential speed gradient is below the first critical gradient value everywhere in the boundary layer as well as within the main flow. This should be the typical case where the PRANDTL-KARMAN-POLHAUSEN should apply. Unfortunately the boundary layer is very thick compared to the cylinder radius. The calculated profile may be over the main theoretical flow speed by more than 50% at the boundary layer thickness distance.One of the many curves obtained is presented thereunder. It is possible to reduce the maximum speed by a similarity transformation. However, the connection is no more complying with the null value of the speed derivatives so that a part of the momentum remains outside the boundary layer, and this is not in line with the hypothesis used to calculate the boundary layer thickness. For q=115.8°, e=5, V0=0.0000625m/s one obtains L=2.39 and d=0.0072m.




But the worth is that so thick is the boundary layer that the mass conservation principle is no more coped with. As the wall speed is null and as it increases very slowly, an overspeed occurs before the boundary layer thickness is reached. It may be thought that the separation occurs by excess of centrifugal acceleration when the boundary speed exceeds the theoretical speed always balancing exactly the pressure drop.


It may be reminded that the existence of a kinetic friction for so low Reynolds numbers would make the separation occurring at 80°. After all this situation has no engineering interest.


36.2 Low Reynolds numbers (10 <e < 50)


The only change against the previous case, is that the speed gradient is now above the first critical value within the boundary layer. Although this case has no more engineering use than the previous one, the separation point was calculated assuming that all the speed gradient is covered by the wall layer made of HELMOLTZ' tubes; the remaining part of the boundary layer is under dynamic friction condition. The code LAM1NAP.BAS allows for calculating the separation point some fraction of degree after the maximum speed of the main flow reached for q=90°.


36.3 Karman street (50 <e < 5000)


The first critical gradient is reached within the main flow as soon as e=50 close to a 90° azimuth. This value is reached very fast upstream as the speed varies with the azimuth sinus. The speed law may be considered as the sinusoid of a lower angle (ratio among 82 and 90) with a lower module (see curve §34).


The KARMAN-POLHAUSEN method applies. However, the speed gradient within the boundary layer reaches the upper critical gradient value at least within the wall layer. The code LAMNNAP.BAS using two values of the kinetic viscosity allow for calculating the separation point in that case. The separation occurs immediately after the speed maximum at 82°.


The wall layer should be made of rotating particles while the upper layers are made HELMOLTZ's tubes. It may be thought that these tubes are growing along the cylinder so that they are visible in the wake.


Another problem cannot be hidden.


From the shore, one may hear the skipper shouting "de l'eau" (that skipper only speaks French) in order to obtain his right to pass first the buoy, just before he plunges in the cockpit of his Star, pushing the tiller, while the sail boom sweeps the deck.


How the upper vortex will inform the lower one that it is now its own turn to go? And what will do this other one while waiting?


In fact, the vortices are generated from the upstream flow before the leading point. There, within the main flow, the first critical gradient is reached, on each side of the axis, but the sign of the gradient is the opposite on each side and in addition it is respectively the opposite of the speed gradient sign along the cylinder wall. So that the lower vortex will roll up on the cylinder upper wall, while the lower vortex will roll down over the lower vortex then along the lower wall of the cylinder.


36.4 Laminar flow (5 <e < 2 to 300 000)


When e=5000, the speed gradient within the main flow reaches the second critical value near the wall for a 90° azimuth. There also the critical value is very fast reached upstream for the same reason. The maximum speed is reached at 82°. The separation calculated with the code LAMNNAP.BAS with the upper kinetic viscosity everywhere, occurs also some fractions of degree after the maximum speed at 82°.


36.5 Turbulent flow (e > 2 to 300 000)


The boundary layer thickness is very small. The use of a polynomial speed profile will lead to an immediate separation just after the maximum near 90°. The reason why the profile using a speed ratio to the n remains unexplained. Nevertheless this profile gives a separation at 120° for n=0.2, while it is assumed that the wall layer is made of very tiny particles ( not far from molecules) with a slipping coefficient much lower than calculated in § 15.


The Code used is CYLTU.BAS.


36.6 Turbulent transition of the flow along a plane


The upper critical gradient is reaches within the boundary layer of the flow along a plane for:



It is no more possible to neglect the term including the particles radius because the second derivative is very large. The upper limit of the radius of particles so that the speed gradient becomes positive and then reaches the upper critical value, is d/300 that is to say of the order of magnitude of 1mm. For this value the flow becomes turbulent by destruction of the laminar layer structure as a result of the generation of additional rotating particles within the fluid nooks.


The transition from the laminar flow to the turbulent flow within the flow along a plane can only involve the boundary layer because there is no gradient at all outside. Thus it appears again that it is necessary to determine the particle radius to obtain quantitative results.



41 Relative speeds within the fluid


41.1 Within the wall layer

a) tangential relative speed

(the solid body rotation is deducted)



b) radial relative speed




41.2 Within the fluid

Values were calculated in §31.

a) tangential relative speed



b) radial relative speed



42 Calculation of the moments


42.1 Within the wall layer


a) tangential friction on the wall side:               


b) tangential friction on the fluid side     :          


c) radial friction                                              


42.2 Within the fluid


a) tangential friction                             


b) radial friction                                              


43 Overall moments


43.1 Overall equation

a) Within the wall layer



b) Within the fluid


43.2 Replacing Du par their value


a) Within the wall layer



b) Within the fluid (while neglecting terms including ap):


43.3 Bringing friction within the general equation:


In this case, all the derivatives related to the azimuth are null and so is Vr.


a) Within the wall layer (while neglecting terms including ap):



This expression gives the angular speed of the wall layer as a function of the angular speed of the bucket as far as both the slipping coefficient and the fluid rotating particles are known.


b) Within the fluid):




When the flow is permanent, the solid body rotation is of course a particular solution of this equation. The general solution is obtained after the following variable subsequent changes:




where u1 is the particular solution related to y=ar (solid body rotation)






The solution is well-known, nevertheless the computerised solution of the Bernoulli type is precise enough for the purpose of this report (Code HELIUM.BAS).





43.4 General case


The second and third derivatives are preponderant when r is small. The general equation writes as follows:




This equation may be integrated by a threefold fourth order Runge-Kutta. Nevertheless it is necessary to know before both the slipping coefficient and the fluid particles' radius otherwise there is always a couple of their values allowing to calculate a surface fall where intended.


44 Results


44.1 Reminding the experimental results


When the bucket containing superfluid helium is set in rotation, helium first remains at rest. The measured surface curve shows that all the helium mass contained in the bucket rotates like a solid body.


At a critical value Wc1 = 3x10-3 rad/s with a bucket radius of 0.01m, a single vortex appears in the bucket axis. Then for larger angular speed, an array of vortices is formed. The photographs taken of the bucket show a vortices' line, roughly spiral at the beginning, evolving towards disorder although the related report (see chapter 60 References) does not state whether is natural or the result of the vibration induced by the camera.


This situation persists up to a second critical value Wc2 = 1012 rad/s for the same bucket radius when the cores start to overlap.


44.2 Construing these results by kinetic friction.


No reference is made there to any assumption on the nature of liquid helium. Only one single fluid is assumed to exist, but this fluid involves kinetic friction although the relative critical gradients and both the upper and lower kinetic viscosities should be very small.


The lower critical gradient appears at very low bucket angular speed. As the gradient is the result of a wall effect, there is always a wall layer made of rotating particles or molecules (atoms for helium).


The same occurs in capillary tubes. If the slipping coefficient is small enough, the wall layer may absorb the whole speed gradient. This is achieved when the kinetic viscosity is very low. Thus the viscosity has no more influence inside the fluid outside the wall layer. The fluid appears not to have any viscosity, mainly when the particles are atoms.


Let us come back to the bucket. As small as may be the kinetic viscosity, the wall layer always has a tangential speed on the inner side, (in the capillary tube this speed is the flow speed). Thus the inner fluid is always set into rotation, and according to the equation there under this is the solid body angular speed.


For higher angular speed, the tangential speed gradient reaches the upper critical value. The kinetic viscosity is increased accordingly and the slipping coefficient is lower than before. The simplified equation (Bernoulli type) leads to a free surface curve identical to the vortex' one for kkf=0.3. Nevertheless it shall be noticed than the surface falls sharply already for higher value of kkf.



 As af is not known, nothing more can be added, and mainly the general equation would not give more information. Nevertheless it could be thought that the upper critical gradient value is reached within the fluid progressively at smaller distance from the axis. Thus it may happen that the helium motion comes to the KARMAN street configuration. If a Reynolds number of 1000, fully within that configuration, then the kinetic viscosity (the upper one) may be as small as ten to the minus 3 lower than the water kinetic viscosity. Such a value may be found to high according to some indications mentioned by the references, but it shall be reminded that this is not the value of the dynamic viscosity but the kinetic viscosity, and their ratio is deeply depending upon the slipping coefficient value.


For much larger bucket angular speed, the transition between laminar and turbulent should appear by local particles peripheral tangential relative speed exceeding the upper critical gradient value. However the way this leads the vortices to overlap remains unexplained. 


Note: All the codes have been developed in QUICKBASIC, including a good editor, now improved by VISUALBASIC, and a compiler as fast as TURBOPASCAL, although BASIC language is very poor as it does not include any variable internal validation and is not intended for engineering use.


51 Equations of the whirl-well flow


The codes PTAVEVO  and  PTSANVO are identical but the boundary conditions are dedicated to each case.


Initialisation shall be done within SUB ENTREE procedure. The options are details in the header ( they are in French language) Two of these options are intended for testing the trends of results according to parameters' value when they have no impact beyond one of the two distances from the axis where the calculation begins. The full run of the code save all the value at both these predetermined distances so that they are automatically loaded when the code is ran at one of those distances.


The method used is based on finite elements on a double mesh (2dR,2dq). The values of the variables are taken at the middle point 2 or 3 according to the integration direction chosen once only for each code. The step is nevertheless (dR,dq). The value at points sup3 or sup4 in line with the integration direction, are calculated by the secant methods in the case of the whirl-well flows both with and without vortex. (This is not the case for the cylinder as explained hereafter.).


 'Mesh schematic



           '                     [sup2]

           '                       :

           '                       ^

           '                       :

           '     [2I]--<---[2=4I]-----------[4]

           '                        :                      :

           ' itert      I        V  en cours   ^ dT*R:

           '  :                     :                      :

           '  :  [1I]------[1=3I]-----<------[3]--->---[sup3]

           '  :                   =2K                  :    -dR

           '  :                    :     K            v

           '  :                    :                    :

           '  :                   [1K]-------[3K]



(en cours = being processed)


These codes do not include any stabilisation feature. They are stable by themselves provided the boundary conditions are defined with a sufficient accuracy far enough from the axis. The optimum distance allowing a good stability was obtained by testing. Any change in the boundary conditions is a very fastidious operation. At least, the boundary pressure P3# shall be set to 0# after any change as described in the procedure included in the SUB ENTREE.


The code may be run out without any kinetic viscosity ( there are no mean to include dynamic viscosity of course) nevertheless the Bernoulli method to calculate the free surface level shall be chosen: in that case the vertical step correction disappears as the vertical speed is set to 0#. In the other case Bernoulli is not applicable; it is a global method and there is no reason to think that the upper part of each step coincides with the same stream line along the horizontal iteration. The vectorial method applied to the equipression surfaces was installed but it does not work correctly probably because the steps are not constant along the horizontal iterations.


During the first tests devoted to the effect of the kinetic moments alone, the accuracy has been improved by correcting and advancing the values given by he secant method. As the solution is not far from a polynom, this is very efficient, but it was not necessary for the calculation related to the kinetic friction and this feature is not operated.


As for all codes involved by this report, the results are saved on a text format on the A: floppy disk drive at the end of the run. The related files may be read by NOTEPAD of WINDOWS or any by other text processor including a DOS text format importing driver. A paragraph mark or any other separator readable by the spreadsheet used shall be added after each value. This fastidious work may be accelerated by a macro when available, only when the figure format and length are identical all over the file. (the curves within this report were obtained by EXCEL4, series' name could not be translated in English; the comments of some curves improved with DESIGNER are translated, the same apply to drawings).


52 Equations of the flow around a cylinder



The equations are fully unstable whatever is the accuracy of the boundary conditions. The secant method cannot be improved as the derivatives' signs are changing. It has been tried to improve the situation by changing the correction sign in line with the second derivative. It was not accurate enough so that the first derivative is used to calculated the values at point sup3 or sup4 according to the case. The results are impaired by this feature as soon as the derivative of the calculated flow differs too much from theoretical solution. Nevertheless, only the point where the derivative sign change is searched. It is the point where speed begins to fall.


Initialisations are made within SUB ENTREE. The step shall be taken small enough: no more than 0.00001#m and sometimes less, for instance for e=5000 where both kinetic viscosities have a significant impact respectively in the main flow and in the boundary layer. The saving features are identical to the codes thereunder. There is no choice of the distance, but a choice in the step and the distance is changed accordingly.


53 Equations of the superfluid helium



This code is based on a double implementation of a forth order Runge-Kutta method applied to a Bernoulli type differential equation. There are no stability problems but some singular points. The solid body rotation is not a solution of the Bernoulli type equation because it disappears when changing the variable just before. Of course it remains a solution of the motion equation.



54 Polhausen and modified Polhausen methods



The code POLHA50 used the well-known Karman-Polhausen equation by a single forth order Runge-Kutta calculating the derivative of L#.


The codes LAMNNAP and  LAM1NAP.BAS are similar to POLHA50 but they are based upon the equation giving the derivative of L# with a wall layer speed different from 0#. The first only consider one single wall layer below a classical viscous fluid ( dynamic viscosity) although the second one involved a fully layered boundary layer with two possible kinetic viscosities according to the configuration calculated and entered within SUB ENTRY. These two codes require very small angle step ( no more than 0.0001# degree and even less near the stating point always taken at the maximum tangential speed azimuth where L=0#). Several steps are predetermined within SUB ENTRY, but they shall be referred to within the WHILE loop within the main program in order to be used.









Hydraulique générale




La couche limite




Introduction à l'étude de la couche limite

Gauthiers Villars


IG Maillard

Cours de Mécanique des fluides




Les fluides à spin

Gauthiers Villars


Le Fur

Couche limite laminaire



Brun,Martinot alt

Mécanique des fluides



A.Gary and alt

A technique for photog.vortex in rot superfluid

Jo of low temp



A microscopic theory of vortices in superfluid




Vorices in rotating superfluid He3

Phys rev



Rotation of a tangle of quantized vortex line HeII

Phys. Rev.Letters


Guo Zhong Hen

Spins in deforming continuum

Mart Nijhoff



Classification of axisymmetric vortices in He3

Hels Un Tech


E. Sonin

Vortex oscillations of rotating superfluids

Rev of Mod phys



Quantized vortices in He3

Rev of Mod Phys


Ph.Petitjean alt

Instabilité des couches limites parois concaves



P.Gérard alt

Résultats récents sur les fluides parfaits incompr




Vortex model with superfluid and turb

Jo of statis Phys



6th order polynom for laminar boundary layer

Meca appli



Quantized vortices and turbulence in HeII

Ann Rev Flu mech



Slow modes and pining in a vortex array He3

Europhys letters


 J. Nebres

Single scale surface perturbation on a cylinder

Exp Fluids



Stability flow around a cylinder

Jof applied math



Vortex dynamics and production of Reynolds st.

Jof Fluid mech


C.Airiau alt

Stabilité linéaire des couches limites

La reche aérosp


P.A. Durbin

Eddy viscosity transport model turbulent flows

Phys of fluids


H.Abarbanel alt

Vortex filament stability and boundary layer High Re

Phys rev


Geropp alt

2D body flow with wake and wall effect

Zeits ange M&M



Couche limite























Physical modelling

of volume waves within

free surface liquids















                     June 2008



1  Introduction


This report is related to the calculation of the propagation speed of volume waves within free surface liquids. Volume waves are resulting of a change in the fluid free surface level. They are not linked to the compressibility of the fluid.


2  Modelling of volume waves within free surface liquids


The basic model chosen by the associated engineers is made of vertical plates. Distance between plates is the same when at rest. They are linked at top and bottom by springs and remain parallel.


The plates, allowed an unit mass m, are moving according to the dynamics fundamental equation :


                 d2 Xp

            m                 =   - Â (Xp - Xp-1 )  +  Â (Xp+1  - Xp)



where Xp is the displacement of the plate number p related to its position at rest
 xp0  = p l0 


The propagation speed of waves within this model is equal to : l0 ÖÂ /m ,
where l0 is the initial distance between plates, m the mass of each plate and
 the stiffness of each spring.


The fluid model is obtained by replacing the springs and the mass of the plates by an identical mass of liquid within each of the cells between the plates. The force of the springs is replaced by the variation of the liquid height within the cells when moving.





   p(p-1)   pp                   pp       p(p+1)                    p(p+1)


    H(p-1)                                  Hp                             H(p+1)       



position  x(p-1) = (p-1)l0         xp = p l0           x(p+1) = (p+1)l0

displacement  X(p-1)                                  Xp                         X(p+1)


Continuity equation writes :


H0 l0 = H(p-1) (l0 + Xp - X(p-1)) = Hp (l0 + X(p+1) - Xp


Horizontal forces acting on the plates of cell number p write:


ρ g (l0 + Xp - X(p-1)) (Hp - H(p-1))                                                                                   



ρ g (l0 + X(p+1) - Xp) (H(p+1) - H p)



The equation of the fluid model with vertical plates is :

             1      d2 Xp                         ( 2 Xp - Xp-1 - Xp+1  )

                                   =   - Hp-1                                                        

             g       dt2                       (l0+Xp+1-Xp) (l0+Xp-Xp+1)


This equation gives, by analogy with the spring model :


V =  ÖgH


3 Limit of validity of the parallel plates model.


The calculation performed within the previous paragraph includes a simplification limiting its validity. A pressure difference of pressure on each side of the plates is resulting from the level difference between each side of a plate. This pressure difference is assumed to be the same from the top to the bottom of the plate. First, the vertical acceleration of the liquid within cells has not been taken into account. Moreover, it has been assumed that the pressure difference is established instantaneously over all the height of the plates. This is only acceptable when the time needed to establish that pressure variation could be neglected with respect to the free level variation time scale.


In other words, The volume wave period shall be much higher than the time needed to establish the pressure variation over the height of the plate :


            T >> H/a                     where a  is the speed of sound within the liquid.


            λ >> (H/a) ÖgH 


The associated engineers fail to understand the justification of the relation proposed by many books where the second term is limited to H.


They cannot understand how the time needed to establish the pressure might not play a part.


There is no condition on the liquid height. The propagation speed of waves within free surface liquids is valid for both the ocean volume waves and for shallowness canals.


The model is valid for ocean deepness of 5000m when the wavelength is over 150m. This is typical of Tsunamis.


It is valid as well for channel 10m deep when the wavelength is over 10cm.


The propagation speed of volume waves is related to a critical value of the bodies moving within fluids. This is similar to sound speed. But the shock waves, which are compression waves, are replaced by volume waves associated to a variation of the free surface level.


The free surface fluid flow is very similar to a wind-tunnel flow where the body is motionless.


For a given water height within a channel, the volume wave propagation speed is characterising the transition between torrential and quiet flows..


The calculation of the canal critical speed is not performed presently on the basis of an undulatory phenomenon. The calculation is rather performed by considering a level raising motion. Thus, there are no vertical accelerations to be taken into account. There is only horizontal accelerations exactly as for the calculation of the speed of volume waves. The calculation conditions are very similar so that it is not surprising to found the same result.


Whatever is the deepness, waves not complying with the wave length condition are surface waves. This is the case of swell. In that case, the calculation shall take into account both the vertical and the horizontal accelerations.


It would be interesting to calculate the wave speed for the model proposed by the associated engineers in the April 2008 report. The global method proposed presently in all books could be used for this model and will of course give the same result. But the calculation of accelerations within each cell, within the model of the associated engineers, is not that simple. They abandon the attempt.


4  Belarras, breaking solitary waves


As a result of the calculations hereunder, Belarras and breaking solitary waves are volume waves, breaking when a deepness change occurs. This is similar to a Cherenkof effect. The swell wavelength shall be over the limit calculated by the associated engineers in relation with the deepness. This condition involves a high wavelength. This occurs within ocean tempest when an opposite current reinforces the swell.


As far as Basque’s Belarras are concerned, The swell is resulting from high sea tempest in the Bay of Biscay. The deepness needed is only reached during equinox high tides.



5 Conclusion


The associated engineers succeed in making the link between volume waves in deep sea and the shallowness canal waves. They explained why the Froude number is common to both cases and also to the propagation of a level raising within a canal.


Additionally, they determined the validity condition of the volume waves speed calculation. This is the transition condition between swell and volume waves.


They determined in the meantime, the process and the condition for swell to be a volume wave instead of a surface wave. This was the main objective to explain the Belarras.


Nevertheless, the associated engineers give up for the last objective. The calculation of the friction within each cell is rather intricate. Moreover it appears that it will not be possible to compare the friction calculation resulting from the de Gennes flows friction concept and the present theory relying on friction between solid. This cannot give significant results because of the wave dispersion during propagation.

















de la houle


















April 2008



1 Introduction


La surface marine, agitée en tous sens, n’est guère propice aux visions simplifiées que permettent les outils mathématiques. La conception des navires et des ports se contente de quelques données accumulées par l’expérience. Si l’on excepte les Belarras, aucun besoin nouveau n’est exprimé. La thèse des ingénieurs associés, exposée dans la présente note, n’a donc, là encore, qu’un caractère pédagogique.


L’origine de ces réflexions vient de l’évocation de trajectoires des particules fluides dans le cadre des théories existantes. Des spécialistes de mécanique des fluides ne peuvent pas ne pas éprouver une forme d’étonnement au spectacle des croisements des trajectoires des particules fluides. Cette note résulte aussi de la nécessité de disposer d’un modèle reposant sur la mécanique des fluides pour l’analyse du phénomène des Belarras.


Avant de proposer une solution, les ingénieurs associés ont établi une liste des phénomènes ondulatoires connus dans les fluides.


Cette note est la première des trois dédiées au problème de la houle. La seconde note sera relative à la vitesse de propagation des houles dans le cadre des simulations proposées par les ingénieurs associés. Enfin, la troisième portera sur l’amortissement des houles. Les frottements seront évalués à partir des équations de Navier-Stokes, puis de l’extension de la thèse du professeur de Gennes à l’ensemble des écoulements laminaires, conformément à leur note de 1994. Cette approche, comme on sait, consiste à considérer que les frottements dans les fluides ne résultent pas des vitesses différentielles entre éléments parallélépipédiques, comme entre deux solides. Il s’agit en fait des vitesses différentielles angulaires entre particules fluides, mises en rotation par les frottements. Les écoulements de Gennes se limitent à la mise en rotation pariétale. L’objectif est de tenter une nouvelle validation de l’approche « cinétique » des frottements par opposition à l’approche dynamique classique.


2 Les ondes dans les fluides


Il existe, curieusement, davantage de types d’ondes dans les fluides que dans les solides, bien que les fluides n’aient pas d’équivalent des ondes transversales. Une certaine striction peut se produire dans les fluides très visqueux, mais la viscosité s’oppose à la propagation qui est, quand même, la caractéristique commune aux phénomènes ondulatoires.


2.1 les ondes sonores


Les ondes sonores sont des ondes de pression. La propagation de ces ondes est étudiée sur la base de la théorie cinétique des gaz. Elles résultent de la compressibilité du fluide. Leur utilisation pratique est particulièrement vaste. Les coups de béliers dans les conduites forcées font évidemment partie de tous les traités d’Hydraulique. Leurs conséquences sont essentielles dans les domaines de l’aérodynamique et de la conception des réacteurs et des tuyères.


Elles sont modélisées dans tous les ouvrages par la propagation d’une onde de compression dans un ressort.


Leur vitesse de propagation dans l’eau de mer s’élève à 1500m/s environ (5400km/h). Il n’y a pas de direction de propagation privilégiée.


2.2 les ondes de gravité de surface, les houles marines


La seconde force de rappel qui permet la transmission d’ondes est la gravité. L’oscillation qui se propage est donc verticale, mais elle se propage horizontalement à la surface libre des fluides.


Elles n’ont pas de modélisation physique, mais des présentations mathématiques diverses.


Elles se propagent, très approximativement, à une vitesse égale à la racine carrée du produit de g par leur longueur d’onde.


2.3 les ondes internes en milieux stratifiés


La force de rappel conjugue une variation de densité du fluide et la poussée d’Archimède liée à la gravité. La principale cause de stratification est d’origine thermique. La stratification n’est pas nécessairement verticale, mais l’oscillation est verticale. Ce type d’onde revêt une importance toute particulière dans les installations nucléaires, par exemple, caractérisées par des températures élevées. Les dispositifs hydrauliques de sûreté ne sont pas utilisés en fonctionnement normal. L’eau stagnante présente des gradients thermiques élevés.





2.4 les ondes capillaires


La capillarité est la quatrième et dernière force de rappel susceptible de produire des ondes dans les fluides. Ce sont des ondes de surface. La célérité de ces ondes diminue quand la longueur d’onde augmente.


2.5 les ondes de canal, dites de faibles profondeurs


Il ne s’agit pas à proprement parler d’un phénomène ondulatoire. Les ondes dites de faibles profondeurs sont la propagation d’une surélévation du niveau de l’eau en amont de nombreux phénomènes. Les exemples vont du mascaret, lié aux marées, à la fermeture des vannes dans les canaux.


Les ondes de canal se propagent à une vitesse égale à la racine carrée du produit de g par la hauteur initiale de l’eau dans le canal. Cette approximation n’est valable que si la surélévation est faible devant la hauteur d’eau. Il s’agit d’une application directe des équations de la mécanique des fluides incompressibles.


2.6 les ondes volumiques, les Tsunamis


Ces ondes sont considérées comme des ondes de canal et sont appelées « ondes de faible profondeur » dans la littérature. Leur vitesse de propagation est celle des ondes de canal. La profondeur des océans conduit cependant les ingénieurs associés à s’interroger sur la validité d’un concept développé pour les faibles profondeurs.


La propagation des marées dans le plateau continental est considérée par les ingénieurs associés comme une telle onde.


2.7 les Belarras, les déferlantes solitaires


Ces vagues se forment dans des conditions très mal connues. Elles ne peuvent se confondre avec les barres d’embouchure des fleuves. Le déferlement des houles résulte, dans ce cas, de la présente de barres de sables constituant des hauts-fonds qui provoquent le déferlement. Les Belarras se produisent en eau profonde. La position actuelle des ingénieurs associés est que les Belarras sont des effets Cherenkof, c’est-à-dire provoquées par une modification brusque de la vitesse de propagation des ondes volumiques. L’analogie des équations des écoulements transsoniques dans l’air et des écoulements transcritiques dans les canaux, et donc entre les rôles respectifs du nombre de Mach et du nombre de Froude, constituent la motivation essentielle des ingénieurs associés. Toutefois, les équations dans l’eau sont établies pour de faibles profondeurs. C’est dans ce cadre que s’explique le passage des écoulements tranquilles aux écoulements torrentiels. En sorte que la signification du nombre de Froude pour les grandes profondeurs reste à expliciter.



3 Les théories de la houle


De nombreux mathématiciens se sont intéressés à la houle. Ils se sont efforcés de montrer que leurs solutions sont conformes aux équations de la mécanique des fluides.


Le modèle le plus connu est la houle rotationnelle trochoïdale de Gerstner. Les particules d’eau se déplacent sur des cercles fixes avec une vitesse angulaire constante. Leur vitesse tangentielle réelle au point haut coïncide avec la vitesse apparente de la propagation des crêtes de la houle. Le rayon des trajectoires décroît de façon exponentielle avec la profondeur. Enfin, à un niveau donné, les particules se déplacent sur leur cercle avec un décalage proportionnel à la distance entre les centres des cercles.


Ces conditions sont conformes aux équations de la mécanique des fluides et la surface libre est bien équipotentielle.


La houle irrotationnelle de Stokes est définie par un potentiel de vitesses conforme aux équations de la mécanique des fluides. La surface est également équipotentielle. Les particules d’eau décrivent des cercles exactement comme dans la solution de Gerstner. La surface libre est également trochoïdale. Mais le caractère irrotationnel de la houle de Stokes exclut la présence d’une distribution de tourbillons qui caractérise la houle de Gerstner.


Les autres solutions sont des variantes de ces deux types de houles mathématiques.


Pour comprendre que la notion de trajectoires des particules d’eau, fondamentale dans ces solutions, ne peut avoir aucun rapport avec la mécanique des fluides, il convient de prendre un exemple.


Le liquide contenu dans une bouteille pleine n’est l’objet d’aucun mouvement pourvu qu’elle ne soit soumise qu’à des accélérations négligeables devant les frottements. Les particules du liquide contenu dans cette bouteille ont néanmoins une trajectoire, approximativement décomposable en sinusoïdes, lorsqu’elle se trouve dans la poche d’une personne qui marche. On peut lui attribuer un tangage et un roulis, plus ou moins accentués, ce qui n’est pas nécessairement incompatible avec le fait que la bouteille soit pleine.


Le liquide contenu dans la bouteille respecte toutes les conditions vérifiées par les houles mathématiques. Pourtant, il est sans aucun intérêt de penser que le comportement de ce liquide est entièrement conforme aux équations de la mécanique des fluides. Les trajectoires des particules du liquide contenu dans la bouteille n’ont aucun rapport avec la mécanique des fluides.


Il en va de même pour la houle. La notion de base de la mécanique des fluides n’est pas la trajectoire, mais le filet fluide. Les particules ne sont pas considérées isolément, mais comme appartenant à des filets fluides. Les équations de la mécanique des fluides ont été établies pour des filets fluides, mais en aucun cas pour des trajectoires de particules. Il est, en particulier, totalement exclu que des filets fluides se croisent, ce qui est parfaitement possible pour des trajectoires. Les trajectoires relèvent de la mécanique newtonienne, mais en aucun cas de la mécanique des fluides. Il serait absurde de vouloir appliquer les équations de Navier-Stokes aux mouvements relatifs des particules d’eau sur leur trajectoire respective. Les frottements se produisent entre filets fluides et en aucune manière entre trajectoires des particules fluides.


Bien sûr, la théorie cinétique des gaz utilise la notion de trajectoire. Elle ne peut être complètement dissociée de la mécanique des fluides. Sans la théorie cinétique des gaz, la notion de pression ne serait qu’une fiction. Une erreur très fréquente est de penser qu’un fluide parfait n’exerce aucune action sur un corps en translation dans le fluide. C’est le paradoxe de d’Alembert. C’est une profonde erreur. Il n’a pas été possible d’écrire, à ce jour, des équations de la mécanique des fluides qui tiennent compte de la nature même de la pression. Le paradoxe de d’Alembert résulte de cette lacune. Il faut donc s’appuyer simultanément sur les deux approches pour comprendre que le paradoxe n’est que mathématique. Physiquement, la vitesse de déplacement du corps dans le fluide augmente d’autant la vitesse quadratique moyenne des particules du fluide à l’amont et la diminue à l’aval du corps. Cette vitesse étant la cause de la pression, celle-ci se trouve donc augmentée à l’amont et diminuée à l’aval. Il y a donc un effet des fluides sur les corps en mouvement dans les fluides, même en l’absence de traînée de frottements et a fortiori de traînée d’ondes.


La conformité d’une solution, même irrotationnelle, aux équations de la mécanique des fluides, n’est ainsi nullement une preuve de sa validité.



4 Les modélisations de la houle


Les phénomènes ondulatoires longitudinaux sont modélisés, traditionnellement, par des ressorts. C’est le cas essentiellement des ondes sonores. Cette simulation n’apporte rien en ce qui concerne la houle. Les ingénieurs associés proposent un modèle physique utilisant également des ressorts, comme dans la théorie de l’élasticité. Les ressorts peuvent être associés à des amortisseurs pour l’étude des frottements, de manière semblable aux modèles de la plasticité.


Le modèle des ingénieurs associés est constitué de plaques fines verticales montées sur rotule en pied et reliés par des ressorts en tête. Les plaques sont planes et indéformables. Les intervalles entre plaques sont remplis d’eau. Dans un premier temps, le poids de l’eau est négligé. La simulation est réalisée par le tableur Excel avec une centaine de plaques. L’ensemble est animé par une action sinusoïdale entretenue. L’écartement des plaques étant variable, le niveau d’eau dans chaque cellule est donc variable.


Les « trajectoires » des particules d’eau contenues dans chaque cellule sont bien des cercles. Vues de l’extérieur, les particules d’eau décrivent des cercles; comme les particules contenues dans une bouteille d’eau qui décrirait un cercle, mais les particules n’ont, au sein de leur cellule, du point de vue de la mécanique des fluides, que des mouvements verticaux liés à la variation du niveau dans la cellule, et en conséquence, également, de légers mouvements transversaux. Les surfaces libres de l’eau, dans chaque cellule, se répartissent, bien évidemment, sur une trochoïde.


Le problème de ce modèle est la discontinuité créée par les rotules. Si les cellules sont ouvertes en bas, il y a nécessairement des échanges avec l’eau située en dessous. Aussi les ingénieurs associés ont essayé un modèle semblable dans lequel les plaques de séparation sont encastrées en pied et déformables. L’épaisseur des plaques peut-être variable du côté de l’encastrement. Le moment transversal d’inertie peut être modifié. La déformation de la plaque peut donc prendre des formes variées. La simulation sur Excel permet de considérer des déformations des plaques souples allant de la solution plane précédente aux formes de courbes de toutes les puissances souhaitées. Les ingénieurs associés ont essayé la forme parabolique et le profil en puissance 3. La liaison avec l’eau sous-jacente peut ainsi être renvoyée à de très grandes profondeurs, en tous cas sans discontinuité différentielle.



La courbe de la surface libre est, bien entendu, toujours tracée en fonction de la position de la surface libre de la cellule et non de sa base.


La simulation réalisée avec le tableur Excel conduit systématiquement à une courbe de la surface libre dissymétrique. La fonction sinusoïdale choisit met la cambrure la plus forte vers la droite. La cambrure est d’autant plus faible que la puissance utilisée pour définir la déformation des plaques souples est élevée.


Ce résultat provient seulement du fait que les calculs des surfaces conduisent, indirectement, à faire la somme de déplacements fonctions de la hauteur d’eau à la puissance choisie. Cette somme diffère légèrement de la puissance de la somme des déplacements. La forme des plaques n’est donc pas exactement fonction de la puissance choisie de la hauteur. Le calcul exact n’est pas trop complexe, mais les choses ont été laissées en l’état car on obtient des courbes équivalentes à celles qui résulteraient d’une variation de la hauteur de l’eau au repos dans les cellules. On peut obtenir des houles jusqu’au point critique de déferlement par cette sorte de simulation de la remontée du fond.


4 Conclusion


Cette première note a permis aux ingénieurs associés de vérifier qu’il est possible de modéliser physiquement la houle. Les résultats correspondent à ceux des modèles mathématiques qui ne sont pas acceptables du point de vue de la mécanique des fluides, même s’ils suffisent parfaitement dans la pratique pour calculer les structures à la mer et vérifier la stabilité des carènes.


L’approche proposée permet cependant le calcul de l’amortissement des houles en appliquant les méthodes relevant strictement de la mécanique des fluides.


Mais l’objectif prioritaire des ingénieurs associés est de déterminer la vitesse de propagation des houles marines dans le cadre des simulations proposées par la présente note. L’objectif évident est de rattacher les ondes volumiques et les Tsunamis aux houles et non aux ondes de canaux dites de faibles profondeurs.


1 Introduction


Although there are no need for improved development of sea swell theories, the associated engineers propose a physical modelling.


Fluids mechanics specialists can hardly accept that trajectories of fluid particles cross one another if it means crossing of fluid threads. On another hand, the associated engineers need a physical model for analysing the breaking high waves such as Belarras.


Before detailing the proposed solutions, the associated engineers issued a list of all known wave-motions within fluids.


This report is the first of the three reports dedicated to swell. The second one will deal with the swell propagation celerity within the frame of the swell modelling proposed by this first report. The last one will be a tentative validation of the angular kinetic approach of friction within fluids as described by the 1994 report of the associated engineers. This approach is an extension of the de Gennes model of heavy oil flow within small pipes. The rotation of the parietal layer of the fluid within de Gennes’ model has been extended by the associated engineers to the full extent of laminar flows. The result will be compared to the dynamic present approach of frictions. The dynamic approach is based upon a concept of friction used for friction between solid bodies.


2 Waves within fluids


There are several kinds of waves within fluids:


2.1 Sound waves


Sound waves are pressure waves. Their properties are quite well described by the kinetic theory of gases. They are a result of the fluid compressibility. They are used in many areas from liquid speed measuring to aeroplanes design.


The model used for such pressure waves is made of springs.


The celerity of sound waves within sea water is about 1500m/s (5400km/h). There is no preferred propagation direction within fluids.

2.2 surface gravity waves: sea swell


The second back action enabling wave propagation is gravity. The oscillation is vertical but it propagates horizontally at the free surface of the fluids.


Such waves have presently only mathematics description but no physical modelling.


Their celerity is about the square root of the product of g by the wave length.


2.3 Internal waves within stratified media


The back action is including both the fluid density gradients together with gravity. Thermal gradients are the main causes of stratification. Stratification may not be vertical but the oscillation occurs always vertically. Safety devices of nuclear power plants with high temperature gradients within motionless water are one of the main areas where such waves occur.


2.4 capillary waves


Capillarity is the forth and last back action enabling generation of waves within fluids. They are surface waves. Their celerity is decreasing for increasing wave lengths.


2.5 canal waves also known as shallowness waves


Those waves are not properly undulatory. They involve propagation of heightening of the water level in canals. They occur when closing water gates as well as tide water level changes in many estuaries.


Their celerity is the square root of the product of g by the depth. The ratio of the actual speed in canals and that celerity is the Froude’s number. The Froude number plays the same part for water canals as Mach number for nozzles.


2.6 volume waves, Tsunamis


Those waves are considered as canal waves. Their speed is approximatively the same as shallowness or canal waves. However as they occur within Oceans deeper than 5000m as well as in the continental shelf about 200m deep, the associated engineers are questioning the validity of such an interpretation.

The associated engineers report dated March 2008 states that the tidal waves within the continental shelf are such volume waves when tide within ocean deeps are an overall upheaval of both the soil and the sea occurring in the meantime in every point of meridians.


2.7 Belarras and breaking solitary waves


Generation conditions of such waves are not clearly identified. Belarras occur only during Spring high equinox tides, about four nautical milles offshore the French Basque coast. They are not linked to any estuary tidal bore.


The position of the associated engineers is presently that such waves are Cherenkof effects occurring when the celerity of waves is sharply changed by sea depth upheaval.


3 Swell theories


There are several mathematical solutions for swell. They comply with the fluid mechanics equations.


The most used is the Gerstner’s rotational trochoïdal swell. Water particles described motionless circles with a constant angular speed. The tangential speed at the upper part of the circle is the apparent swell speed. Circles radius is decreasing exponentially with depth. For a given level, particles are moving along their circle out of phase with an angle proportional to the distance between the centres of circles.


Those conditions are complying with the fluid mechanics equations and the water free surface is equipotential.


The Stokes’ irrotationnal swell is defined by a speed potential complying also with the fluid mechanics equations. The water free surface is also equipotential. Water particles moves along circle as for the Gerstner’s swell and the free water surface is trochoïdal as well. But there is no vortex distribution within water as for Gerstner’s swell.


Other solutions are said to be variant of both those solutions (in fact the associated engineers have no knowledge about those variants).


In order to explain that the water particle trajectories have not the slightest relation with fluid mechanics, the best is to give an example.


The liquid contained within a bottle, fully filled in, has no motion involving the implementation of fluid mechanics equations as long as the bottle is handled carefully so that acceleration effects remain very small against frictions inside the liquid. Nevertheless, the liquid particles do move along trajectories when the bottle is slipped into the pocket of somebody walking along. This fellow may have both rolling and pitching motions. The trajectories of the liquid particles in the bottle are the same as the bottle trajectory. Their motion may be split in sinusoids.


All conditions enabling for implementing the fluid mechanics equations are fully coped with. The free surface of the liquid in the bottle is equipotential. However those motions have not the slightest relation with fluid mechanics.


The situation is exactly the same for fluid particles within swell. The basic concept of fluid mechanics is not the trajectories but the fluid threads. Particles are not considered as material isolated point as for Newtonian mechanics but as belonging to these fluid threads. Fluid mechanics equations have been issued for such fluid threads. Mainly, it would be nonsense to implement the Navier-Stokes equations to calculate the friction within swell using the speed of fluid particles along their trajectories. These equations are definitely only valid for fluid threads. Frictions occur between fluid threads and not between trajectories.


Of course, trajectories play a main part within the kinetic theory of gases. This theory cannot be dissociated from fluids mechanics. Fluid pressure would be a pure fiction if not considered through the concepts of the kinetic theory of gases. Such a distinction leads to one of the most frequent errors when studying fluids. The perfect fluid equations give a null effect of the fluid on a body moving within the fluid. This is known as the d’Alembert paradox. But it is only a mathematical paradox. In fact, the effect of a perfect fluid on a moving body shall be obtained through the implementation of the kinetic theory of gases. The mean quadratic speed of the fluid molecules is increased by the speed of the body so that the upstream pressure on the body is, in turn, increased, and conversely decreased downstream. So that a fluid has always an effect on moving bodies even when not taking into account the friction drag or the wave drag.


Finally, a mathematical solution, should it be irrotational, coping with fluid mechanics equations, is not necessarily a fluid mechanics solution.


4 Swell modelling (for figures and curves, please refer to the French text)


Longitudinal Waves are traditionally modelled by springs. This is mainly the case for sound. This is not applicable to swell. Swell is characterised by vertical motions of water.


The associated engineers propose a physical model based upon thin vertical plates linked by perpendicular springs at their upper part and mounted on axis at their lower part. Plates are flat and indeformable. They initially form a series of identical cells filled in with water. Within this report the weight of water is neglected. It will be taken into account by the next report, in place of springs, to calculate the speed of the swell. Dashpots may be installed, parallel to the springs, to simulated friction losses in a similar way to plasticity modelling.


The cells are actuated by a sinusoidal action. The distance between plates is not constant so that the level of the water in the cells is changing. 


The trajectories of water particles are of course circles. They seem to describe circle exactly as would particles inside a bottle when the bottle is describing a circle, but within each cell, they have only a small vertical motion and a related horizontal motion linked to the motion of the level of the water in the cells. The surfaces of the cells altogether form, of course, a trochoïd.


This model, as the next ones, has been simulated with Excel. Calculation sheets, including formulas, are attached to this report.


This model cannot prevent water motion at the bottom of cells when the bottoms are opened. There is a discontinuity at the axis level.


This is the reason why the associated engineers propose a better model. The axes of the plates are replaced by an embedded part. The inertia module of the plate is variable so that any kind of curve may be obtained by changing the law of deformation of the plate under the action of the springs. The associated engineers tested this model with parabolic and power 3 curves. 


The free surface of the water within the cells altogether described an unsymmetrical curve. This is a result of the calculation method. Distances between plates have been added to determine the top width of each cell. As the displacement is a power of the height of the water in the cells, the total calculated displacement exceeds the exact displacement. Although this would not have been too difficult to be changed, it has been left as it is because it gives a very simple way to consider the effect of a raising of the bottom part of the cells. This occurs when the swell reaches the seashore. It has been possible to obtain curves up to the critical point where the swell breaks.


4 Conclusion


This first report enables the associated engineers to check that it is possible to model the swell with physical devices. The results are similar to those obtained with purely mathematics models.


This physical approach allows for calculating the damping out of the swell by friction using methods fully complying with fluid mechanics principles.


But the main objective of the associated engineers is to determine the celerity of swell using the models they propose within this report. Their objective is to show that volume waves as well as Tsunamis are relevant to swell and in no case of canal waves called in the literature shallowness waves. The Froude’s number has no meaning within deep sea, because torrential flows are irrelevant.


































 March 2008


This report is public. Its use as a whole or the use of any part thereof cannot involve any subsequent right.

Ce rapport n'est couvert d'aucune protection. Son utilisation, en tout ou partie, ne peut générer aucun droit.

1 Introduction


Several theories of ocean tides may be found in Internet. As it seems to be a problem involving Fluid Mechanics, the associated engineers decided to look at it.


Several theories are based upon the idea that tides are very large waves generated in the equator zone.


In fact, it appears that it is not the case. The main part of the tide phenomenon is a result of the Newtonian mechanics principles. There is an overall swelling of the sea level from the Equator up to 50°N and S latitudes. Tides are waves only within the continental shelves where deepness is sharply smaller.



2. Generating accelerations


There are two generating accelerations: the Moon gravitational effect and the Sun gravitational effect. The overall effect of planets is 10 000 times weaker than the Sun effect in the most favourable conditions.


The inertia of the Earth generates centrifugal accelerations as a reaction to the generating accelerations.


As a consequence of the Newtonian principles, the centre of the Earth is in weightlessness condition within its rotations around the gravity centres of the Sun and Earth and of the Earth and Moon yokes.


The rotation of the Earth centre around these centres of gravity does not imply any angular momentum. There are no links between the Earth centre motion and the Earth angular momentum.


The Moon is an exception. The Moon does have an angular momentum linked to its revolution around the Earth. But this is, in no case, a result of the Newtonian principles. This situation may be a result of the solidification of a gravitational buckling. This is an indirect consequence of gravitation.


Thus, the centrifugal acceleration balancing the Moon gravitation at the centre of the Earth is the same everywhere on the Earth.


The same applies to the Sun. There is not any mechanical reason for the Earth to have an angular momentum, bound to its rotation around the Sun.


Ocean tides are a result of the vectorial combination of the Sun and Moon gravitation at the surface of the Earth with the related centrifugal accelerations of the centre of the Earth within its revolutions around the gravity centre of both yokes made of the Sun and the Earth of the Earth and the Moon.


Calculation shows that the centrifugal accelerations shall not be calculated from the distance of the surface of the Earth to the gravity centres of the yokes. Such a distance will multiply by 100 the effect of the Moon. The effect of the Sun would then be negligible. The change will not affect mainly the time of high tides but their height. In the case of Brest (France), taken as reference within this paper, there will be only one maximum per month instead of two as it is the case for the months used in the calculation (January, March and June 2008).


The main result is, of course, well known. There are two cycles per day. Gravitation of the Sun or of the Moon is larger on these asters side than in the centre of the Earth, and lower the other side of the Earth. But the very same centrifugal accelerations are subtracted, in each case, from the gravitation acceleration. The resulting acceleration is positive on the attracting aster side and negative on the other side. The positive acceleration is toward that aster, the negative is in the opposite direction. Thus there is a bulging each side of the Earth.


The soil of the Earth is submitted to the same accelerations.


3. The tide mechanism


The time schedule of tides is mainly a result of the position of the Moon and of its crossing of the mean meridian of the Atlantic Ocean.


The first hypothesis involved a swelling of the sea in the equatorial zone.


The highest swelling would have occurred at latitude corresponding to the Moon declination. It would have been modified by the Sun effect according to its own position. The swelling would have generated a large wave propagating within the Atlantic Ocean. This wave should propagate with a speed of about 800km/h up to the continental shelves.


Such a scenario is fully incompatible with the time schedule of high tides in Brest (France). The volume wave Froude’s speed would be either over 1500 km/h, or below 300 km/h. These speed are the volume waves speed for sea deepness of 20 000m and 800m respectively. But, the mean deepness of the Atlantic Ocean is 5000m. This is not consistent. These mean speeds do not take into account the continental shelf, included in a separated calculation.


In addition, the declination variations of both the Moon and the Sun generate changes in the distance to be covered by the tide waves. They account for one third of the total distance from the Equator to Brest. The result is fully inconsistent with the Brest time schedule of high tides.


Within the graphs hereunder (January 2008), K is linked to the propagation speed of volume wave in the sea (Froude’s speed). K=1,04 is related to a speed of 800 km/h. For K= 0, the tide phenomenon is characterised by an overall swelling from the equator zone up to the North of the Atlantic Ocean.


Damping had been tested. The damping includes both frictions and diffusion of the wave. It has been determined from the Tsunamis damping as measured for Alaska and Chile earthquakes. This had not improved the curves.


As a consequence, oceanic tides are not waves. They are rather an overall bulging or swelling of the ocean up to latitude as high as 50° N and S. The speed of the swelling is about 1800km/h at the Equator. This is the speed of the Moon with regard to the surface of the Earth. The swelling is the same at all point for a given latitude when the moon is passing by. But the cohesion of soil is greater than water. For low depth (<250m), the additional swelling is only some centimetres when it is over one meter for depth about 5000m as it is the case for oceans compared to about 50 cm for the sea bed in both cases. This gap generates a volume wave at the cliff edge of the continental shelf. This volume wave propagates at the Froude’s speed through the continental shelf. The associated engineers are in process of determining the critical conditions for a change of sea level, such as surface waves, to generate a volume wave, within their analysis of Belarras.


This is the only available explanation to the delay between the time swelling is produced and the time the high tide occurs in Brest. This delay is about an hour and a half. This is precisely the duration needed for a Froudian wave to propagate through the continental shelf when the sea is about 150m deep. A more precise calculation should involve the speed of the swelling displacement.



4. Calculations


The implementation of the Newton law is the only calculation done. As centrifugal accelerations always keep their values at the centre of the Earth, they were not calculated. Rather they were replaced by the related values of the gravitation at this centre.


The orders of magnitude of the resulting accelerations at the Earth surface on the side of the attracting bodies and at the opposite side of the Earth are well known:


resulting acceleration of the moon  :           1.2161E-06   m/s²

resulting acceleration of the Sun                 :           5.0575E-07   m/s²

resulting acceleration of Planets                 :           8.2542E-11   m/s²

(total of all planets assumed to be aligned at their shortest distance to the Earth)


Moon and Sun data were found in Internet. Tables used are valid for Paris meridian. Linear corrections were implemented to obtain the needed values for the mean meridian of the Atlantic Ocean (30°W). Tests were performed to check that slightly modified data would not impair the validity of the results within the objective of this paper.


The tables used give the values for each day. Interpolations were performed to obtain the increment for half a day. The step of the calculation is ten minutes. As no better data smoothing was performed, there are small flaws in the curves when high tides occurs near 18H TU, the time of data change in the calculation. Those calculations are not iterative.


MS Excel worksheet was used for all calculations. They are split among several sheets in order to easily validate each step. The time base is from 6H TU to 6H TU, so that there are no risk of error for the Sun. Nevertheless the trigonometric calculation were performed with a parallel base from 0 à 360°. High tides schedule obtained by calculation is thus compensated by addition of 6H (plus 10/60 related to the starting point of the calculation). An additional 2.155 hours is also included in the compensation in order to take into account the angle between the Paris Meridian and the mean Atlantic Ocean meridian. Moreover, 1.5 hour is finally added to take into account the time needed for the tide wave to reach Brest through the continental shelf. (And last, of course, it is necessary to subtract 24h from time to time and to jump to the next day… and not to forget the legal time changes because the time table found in Internet are given in legal time). These compensations are always the same for all the high tide time schedule curves.


The heights of high tides makes use of typical French system: the tide coefficient. Tables give this coefficient in place of height in meter as usual. It is quite interesting because this coefficient is generally unique for each tide all over the country.


The tide coefficients in Brest were directly calculated from the value of the resulting accelerations through a linear transformation. This is a rather rough approximation. Accelerations depend upon the inverse of the square of trigonometric functions. And those functions are not the same for the Sun as for the Moon. Slightly different linear transformations were implemented for the high tides in Brest related to a Moon position on the Atlantic side and on the Pacific side.


The calculations were performed for the months of January, March and June 2008.


4. The curves


January 2008 data was used to validate the approach. The K parameter indicated on the curves is related to the hypothesis of a tide wave propagation from the Equator zone to Brest. This parameter is intended for including various propagation speeds, that is to say to test that solution for various deepness. This solution has been eliminated, so that K=0 for all the curves.


The curves of January 2008 include also an « angle » option. This was a test of the impact of the attracting aster declinations. Although the variation of declinations are trigonometric, a linear variation was implemented using a device intended first for the impact of the declination on the distance to be covered by the tide waves. This does not produce any improvement of the curves. Nevertheless the change was maintained for all curves.


At last, the angular momentum of the Earth within its revolution around the Sun was removed. This is the curve « sans rotation Terre » appearing in the January 2008 tide curves. This is consistent with the same provision made systematically for the Moon so that it has been maintained for all curves.


The compensations detailed within the previous paragraph have been implemented at the end of the calculations. Please note that the high tide times and the related coefficients have been obtained « manually » looking at the calculation results. As explained, these compensations include both the impacts of the units and origin chosen for the calculation and the duration of the wave propagation through the continental shelf (1.5-hour). As also explained, there are two slightly different linear transformations of the resulting accelerations to obtain the tide coefficient, one for each case: the first when the tide is produced by the Moon located on the Atlantic side, the other when the Moon is located the other side round, about half a day later.







This paper shows that it is possible to present the ocean tide problematic in a very simple way. This is fully convenient for pedagogic approaches. It is an opportunity to deepen the concept of the Newtonian mechanics while allowing for a first approach of the angular momentum problematic which is rather more difficult to perceive.


The Ocean tides are overall swelling of the sea level from 0 to + 50° and – 50° latitudes. This swelling is the result of both a deformation of the Earth and of the Sea. These swellings have been calculated and confirmed by satellite levelling. The values are about 50cm for the soil and one meter for the Open Sea level. The tide amplitude within the continental shelf would be negligible without any other action. This amplitude is a result of the propagation of a volume wave generated by the swelling on the cliff of the continental shelf. Thus, the amplitude is independent from the dimension of the shelf. A general additional swelling of the Open Sea is produced by the reflection of the forming volume wave on the cliff itself. This is typically the case both in Alaska and between Madagascar and Africa.


The tide amplitude within the continental shelf and the coast amplitude are higher than the swelling for hydraulic reasons which could be compared to Tsunamis. The continuity equation would give a ratio of 25. This is an additional proof that there are no volume waves in the Open Sea. The volume wave is generated on the cliff. The deepness involved should be about 500m.


Then this swelling propagates as waves through the continental shelves. The speed of these volume waves is given by Froude’s law i.e. proportional to the square root of sea deepness. According to the mean deepness of the continental shelf, the high tide should occur in Saint-Malo (France) 2 hours later than in Brest, 10 minutes before in La Rochelle and 30 minutes before in Saint Jean de Luz, near the Spanish border.


In fact, this is not that easy.


Ocean tide is an intricate problem. But the replacement of the wave propagation hypothesis by an overall swelling opens a way to explain the rather more intricate problem of tides in the Pacific Ocean, although that Ocean is divided in three vertical zones so that it could be analysed in three steps.


Appendices (Attached to the French text):

January, March and June 2008 tide curves for Brest (France).

The first two curves of each month give the high tide for each day of the month. The two other ones give the related French coefficients. Colour codes are indicated on the graphs.














du principe

de Hamilton

en mécanique des fluides



of the Hamilton’s principle

in fluid mechanics















May 2008



1 Introduction


Plusieurs sites Internet exposent le problème de la rotation des cyclones de manière enfin conforme à la réalité. L’accélération de Coriolis, dont le caractère mystérieux a le don de plaire, selon le célèbre jugement d’Erasme, ne joue, au mieux, qu’un rôle marginal dans la rotation des cyclones, et ce d’autant plus qu’à proximité de l’équateur son effet est nul.


La rotation des écoulements de condensation n’est pas le résultat du hasard ou d’une quelconque « loi de la Nature ». C’est un problème d’énergie minimale comme dans la théorie de l’élasticité, ou, si l’on préfère les visions plus mathématiques de la physique, une conséquence directe du principe de Hamilton.


2 Cas des fluides parfaits et visqueux (3 dimensions).

2.1   Applications du principe de Hamilton


NOTA : Dans ces équations, v est la vitesse du fluide en un point donné, p la pression, g la gravité, r la masse volumique. Dans la suite m est la viscosité.


2.1.1 Continuité


            div v   =  0                                                                 (1)


2.1.2 Equation d’Euler (fluide parfait) :


            (v Ñ) v =  -  1  grad p + g                                            (2)      


2.1.3 Bernoulli (le long d’un filet fluide)


             1  v2  +  g z  + p  = Cte  

             2                     r


2.1.4 Conservation de l’énergie (Equation de Lagrange)


L’équation est identique à l’équation de Bernoulli, mais elle est valable dans toute la masse du fluide.


2.1.5 Application au puits-tourbillon.


De (1) on tire :


            vr  =  -  k 



et de (2) :


            p  = 2 k2+  vq2                               (3)

            r  r        r5      r


            p  =  k  (   vq + vq )                        (4)

            r r¶q      r2      r       r 


Si l’écoulement spatial des puits est à symétrie sphérique, il n’en va pas de même de l’écoulement tourbillon qui est axial. L’axe permet de définir le plan principal ou équatorial de l’ensemble des deux écoulements. Le théorème de Poincaré entraîne la formation d’un tourbillon concentré dans la zone principale ou équatoriale ainsi définie. L’équation de Bernoulli donne :


            p  =  1  vq2  +  2 k2                        (5)

            r  r      2  r             r5


Les équations (3) et (4) donnent :


            vq  = - k’              


L’écoulement puits-tourbillon est irrotationnel. Ce genre d’écoulement dérive d’un potentiel.


f(z) = A Log(z) + i B Log (z) 


où a et b sont des constantes. On prendra B = - b² pour définir un sens de rotation et
A = - a² pour définir le sens d’écoulement du puits par opposition à la source.


Le Hamiltonien doit être un extremum. Le principe de Hamilton s’écrit :


            H  =  0           avec      H =  ò dt Smv²

            c                                                t1


dans l’expression de l’action, c représente le paramètre d’une famille de solutions possibles. Dans le cas du puits tourbillon, c’est le rapport des constantes des deux écoulements. La généralité de la démonstration n’est pas affectée en choisissant pour intervalle de temps celui qui correspond à une seule rotation des particules fluides dans le tourbillon, donc la variation de q de 0 à 2p. On obtient :


            H = 2 p a4+b4     



Le hamiltonien est représenté par la courbe ci-après. On remarque que la solution puits intégral, sans tourbilon, est théoriquement possible, mais hautement instable. Les équations des écoulements puits tourbillon étant identiques pour les fluides parfaits et les fluides réels, il apparaît que la théorie n’est nullement conforme à la réalité puisque, d’une part, l’écoulement puits pur peut se maintenir en eau très calme et que, d’autre part, le rapport entre les constantes du puits et du tourbillon n’est pas de un. Ces deux faits viennent confirmer qualitativement l’extension de la conception même des écoulements de Gennes, posant la mise en rotation de la couche pariétale des huiles lourdes dans les canalisations de faible diamètre, à tous les écoulements laminaires, extension objet de la note des ingénieurs associés de 1994. L’application de cette conception était d’ailleurs basée sur les écoulements puits tourbillons. L’extension ne pourrait être justifiée mathématiquement ici que par l’application du principe de Hamilton à cette conception des écoulements laminaires. C’est ce que les ingénieurs associés n’ont pas réussi à ce jour.


La pression s’annule pour la distance rc  telle que :


            p0 = r (  k’  - k   )     

                        r2c  r4c


Dans un domaine très proche de la mécanique des fluides sur le plan purement mathématique, l’élasticité, l’habitude est plutôt d’appliquer le principe de l’énergie minimum, conséquence du Principe de Hamilton, mais beaucoup plus intuitif. On obtient, bien évidemment le même résultat.



2.2   Applications du principe de l’énergie minimum


Entre l’instant  - ¥  relatif à l’écoulement à l’infini et l’instant tc où la pression s’annule, la variation d’énergie cinétique, représentant le travail des forces résultant de la pression, est représentée pour une particule fluide  dm par :


            d Ec     =   1  dm ( vr2   + vq2 )



            d Ec dt  =   1  dm ( k2   +k’2 )  dt

                               2          r4c    r2c 


Sur un cercle de rayon r :    dt  =   rc  dq    


            d Ec t   =    dm 2 p  1     ( k2   +k’2

                                rc           k’      rc2 


k est le paramètre du débit, et sa valeur ne peut donc être une condition de l’énergie minimum. Il doit y avoir au moins une solution pour chaque valeur de k. La dérivation doit donc être faite par rapport à k’ :


            ¶(d Ec t )  =    dm 2 p  1     ( k’2   k2

                k’                rc        k’2               rc2

Le minimum est obtenu pour  k’ =  +  k .



Les équations de la mécanique des fluides ont été établies sur la base de plusieurs hypothèses fondamentales. Il a été principalement supposé que les molécules, ou atomes, n’ont pas de moment cinétique. Ce n’est pas le cas le plus général.


Il convient d’abord de modifier les lois des chocs élastiques de la théorie cinétique des gaz, en ajoutant la transmission des moments cinétiques. Cette transmission ne peut se faire que dans le cadre de la théorie de l’élasticité. Les déformations élastiques doivent comporter une dissymétrie induite par les moments cinétiques des corps lors du choc. La surface de rencontre est gauche au lieu d’être plane. C’est la condition de la transmission d’un moment cinétique transversal : le gauchiment contribue, avec l’aplatissement, à empêcher le glissement. La restitution de l’énergie de déformation suit le processus inverse. Les particules d’un fluide, douées d’un moment cinétique, ont, dès lors, six degrés de liberté. Dans le cadre de la théorie cinétique des gaz, les particules ne rentrent pas dans le concept utilisé dans la mécanique des fluides, mais s’applique aux atomes ou molécules du fluides. Le principe d’équipartition de l’énergie permet une modification radicale des équations fondamentales de la mécanique des fluides, qui conduit principalement à une solution puits-tourbillon à vitesse tangentielle en 1/SQRT(R), au lieu de la forme bien connue en 1/R. Si, malheureusement, l’écoulement n’est plus irrotationnel, il peut trouver des applications intéressantes. Le caractère rotationnel n’est justement pas sans remarquables conséquences comme on le verra dans le dernier paragraphe.



Chaque particule du fluide est donc supposée avoir 6 degrés de liberté


3.1 Continuité


            div v   =  0                                                                  (1)


qui donne comme dans les fluides parfaits sans moments cinétiques :


            vr  =  -  k 



Cette relation est la loi des flux fluides. Elle exprime qu’en l’absence de condensations et d’évaporations internes autres qu’au centre du puits, le flux massique se conserve. Tant que le fluide peut-être considéré comme incompressible, le flux volumique se conserve également.


3.2 Théorème du moment cinétique.


Le théorème du moment cinétique pour un élément de volume dv = rdq ds avec
ds = dr dz, s’écrit :


I étant le moment d’inertie de l’élément de volume par rapport à l’axe perpendiculaire au plan de l’écoulement passant par l’origine des coordonnées cylindriques, W la vitesse angulaire locale de l’écoulement plan.


i est le moment d’inertie des composants du fluide par rapport à l’axe perpendiculaire au plan de l’écoulement passant par leur centre de gravité et w la vitesse de rotation des composants de l’élément de volume autour de cet axe, le produit de ces deux quantités étant sommés dans l’élément de volume.


Le moment cinétique principal peut se mettre sous une forme plus habituelle :





On peut donc écrire :


Les frottements seront négligés dans la suite. Dans le cas du puits-tourbillon cette dernière équation devient :

3.3 Principe d’équipartition.


L’équipartition de l’énergie dans le fluide a pour conséquence que la moyenne des moments cinétiques des particules de fluide n’est pas nulle. Dans les fluides à 6 degrés de liberté, l’énergie cinétique de rotation qui apparaît en raison de la rotation du fluide doit être compensée par un apport d’énergie qui ne peut provenir que des particules elles-mêmes. En l’absence de toute force extérieure, l’équipartition de l’énergie se ramène à l’égalité des variations instantanées des moments cinétiques :

soit :

L’équation du § 3.2 devient :

et donc :

                Vq  =  -   k’      toujours avec   Vr  =  -   k     

                                      Ör                                                       r2


La pression s’annule pour la distance rc  telle que :


            p0 = rk’  - k   )     

                            rc    rc4


Il faut noter que si l’écoulement puits lui-même est toujours irrotationnel, l’écoulement tangentiel, le tourbillon, ne l’est pas. Les frottements devraient donc être pris en compte dans les équations. La solution exposée n’est donc valable que pour les vitesses tangentielles suffisamment faibles par rapport à la vitesse quadratique moyenne d’agitation des composants du fluide, c’est-à-dire par rapport à la célérité des ondes dans le fluide.


Les fluides à moments cinétiques sont composés de particules dotées d’un moment cinétique brownien dont l’énergie de rotation correspondante est égale à l’énergie cinétique d’agitation. Dans ces fluides, la notion de température est exclue, et, puisque les frottements doivent être considérés comme négligeables aux vitesses extrêmement faibles envisagées, les échanges d’énergie que nécessitent les déplacements forcés se produisent par pompage ou apport d’énergie cinétique de rotation à l’énergie cinétique de rotation brownienne.



3.4  Application du principe de l’énergie minimum


Entre l’instant  - ¥  relatif à l’écoulement à l’infini et l’instant t, la variation d’énergie cinétique, représentant le travail des forces résultant de la pression, est représentée pour une particule fluide  dm par :


            d Ec     =     dm (   Vr2    Vq2 )




            d Ec dt  =   dm (  k2   k2 ) dt      avec dt =   rc  Ö rc dq

                                         r’4c       r’c                                                k’  


            d Ec t   =    dm 2 p Ö r’ck2   +  k’2

                                k’                   r’3c           


k est le paramètre du débit, et sa valeur ne peut donc être une condition de l’énergie minimum. Il doit y avoir au moins une solution pour chaque valeur de k. La dérivation doit donc être faite par rapport à k’ :


            ¶(d Ec t )  =    dm    p  Ör’c     ( 2 k’2   k2

                k’               k’2                                             r’3c


Le minimum est obtenu pour 


                        k     =  _______    

                                       r’c Ör’c


Il n’existe donc qu’un seul écoulement puits-tourbillon conforme au principe de l’énergie minimale, mais il faut noter que cet écoulement dépend de rc , et donc de la manière dont s’établit le débit du puits, représenté par k. En particulier, l’écoulement puits seul est exclu n’étant pas stable.



3.5 Transfert d’énergie


Il faut noter qu’une particule fluide située à une distance r du puits, dans un fluide parfait sans moments cinétiques, est animée de deux mouvements de rotation opposés : le premier dû à la rotation d’ensemble dans le tourbillon, le second dû à la variation de la vitesse tangentielle du tourbillon entre les extrémités de la particule fluide la plus proche et la plus éloignée du puits.


Or, dans le puits-tourbillon en fluide parfait, les vitesses angulaires de ces deux rotations sont égales et opposées :


       w1 = Vq     =          k’                            w1 = 1Vq dr /dr    =        - k’   

                    r                         r2                                      2 r          2              r2


Il n’y a donc aucune rotation des particules du fluide. Toutefois, il en résulte une rotation différentielle de particules du fluide qui ne correspond pas au modèle classique puisque le Laplacien est nul et qu’en conséquence il n’y a pas de frottements au sens classique. Cet écoulement est dit irrotationnel. Par contre, il existe des frottements qualifiés de cinétiques, car provenant de rotations relatives qui permettent d’ailleurs d’expliquer l’anomalie liée au soulèvement de la surface libre près de la bonde par rapport à la surface théorique obtenue en ne considérant pas les frottements cinétiques, donc dans ce cas, en l’absence de tout frottement. On peut noter au passage, que cette approche « cinétique » des frottements dans les fluides permet également d’expliquer le comportement des fluides dans leur écoulement autour d’un cylindre et, beaucoup plus fondamentalement, le comportement de l’hélium superfluide dans un cylindre en rotation sans faire appel, en aucune manière, à des considérations probabilistes, entièrement étrangères à la mécanique des fluides, et de résoudre les paradoxes du bi-fluide de Landau. Ce qui résulte, aussi bien, du concept de mise en rotation pariétale des écoulements de Gennes, étendu à tous les écoulements laminaires.


Par contre, dans l’écoulement puits-tourbillon en fluide à moments cinétiques, la vitesse angulaire de la rotation d’ensemble est l’opposé du double de celle de la rotation due à la variation de vitesse tangentielle :


        w2 = Vq     =         k’                            w2 = 1Vq dr /dr    =        - 1     k’   

                       r                       rÖr                                       2 r        2        2  r Ör


Il y a donc bien transfert d’énergie. Il en a été tenu compte dans les équations.


Dans le cas des fluides à moments cinétiques, on peut avoir l’ordre de grandeur de l’énergie pompée dans l’énergie cinétique de rotation brownienne du fluide, en intégrant l’énergie cinétique de rotation de l’écart entre les deux vitesses de rotation ci-dessus depuis l’infini jusqu’à la distance R du puits :


       R                                  R

     ò S ½ i w22 /4  =  ò ½ (2 p r dr dz l) i  (1/4) k’2/r3    =  (p/4) l dz i k’2/R 

     ¥                                  ¥

 l étant le nombre de particules du fluide par unité de volume, i le moment d’inertie de ces particules et dz la hauteur de la zone considérée



4 Conclusion

L’approche des ingénieurs associés pour les fluides réels, par opposition aux fluides parfaits, ne serait pleinement validée que par la détermination du Hamiltonien des écoulements à frottements cinétiques c’est-à-dire par rotations différentielles des particules du fluide selon le concept des écoulements de Gennes et non par déplacements différentiels selon le modèle actuel emprunté à la mécanique des solides. Quant aux fluides à moments cinétiques internes, c’est un tout autre problème qui n’a été ajouté à la présente note que pour être formalisé.



1 Introduction


Condensation or well flows rotation are not occurring as a result of some “law of Nature” or by chance. It is a direct consequence of Hamilton’s principle. It can be considered as well as an implementation of the minimum energy as used within Elasticity theory.


2 Perfect and viscous fluids (3D).

2.1 Hamilton’s principle implementation


Note : within the following equations, v is the speed of the fluid at a given point, p the pressure, g gravity, r volume mass. m is the fluid viscosity.


2.1.1 Continuity


            div v   =  0                                                                 (1)


2.1.2 Euler’s equation  (perfect fluid):


            (v Ñ) v =  -  1  grad p + g                                            (2)      


2.1.3 Bernoulli (along a fluid thread)


             1  v2  +  g z  + p  = Cte   

             2                     r


2.1.4 Energy Conservation (Lagrange’s Equation)


This equation is the same as Bernoulli, but it is valid within the whole fluid.


2.1.5 Implementation to the whirl well flow.


From (1) it comes:


            vr  =  -  k 



and from (2):


            p  = 2 k2+  vq2                               (3)

            r  r        r5      r


            p  =  k  (   vq + vq )                        (4)

            r r¶q      r2      r       r 


The 3D well flows have a spherical symmetry although the whirl flows are axial. The axis defines the main or equatorial plane of the combined flow. The Poincare’s theorem entails the whirl to concentrate in the main plan of the combined flow. Bernoulli’s equation gives:


            p  =  1  vq2  +  2 k2                        (5)

            r  r      2  r             r5


Equations (3) et (4) give:


            vq  = - k’              


The whirl-well flow is irrotationnal. As the Laplacian is null, viscous fluids are the same as for perfect fluids. The flow is deriving from a potential.


f(z) = A Log(z) + i B Log (z) 


where A and B are constants. It may be assumed that B = - b² in order to define the rotation direction and A = - a² for the condensation flow.


The Hamiltonian shall be an extremum. Hamilton’s principle writes:




            H  =  0           avec      H =  ò dt Smv²

            c                                                t1


Within the “action”, c is the parameter of the possible flows family. For Whirl-well combine flows, it is the ratio of the constants. The demonstration remains fully general when assuming the time interval to be limited to one turn i.e. for q increasing from 0 to 2 p. Then it comes:


            H = 2 p a4+b4     



The Hamiltonian variation is given by the curve hereafter. It appears that the sole well flow is highly unstable. Viscous and perfect flows are identical in that case. Thus the theoretical approach is not complying with reality, for a pure well may occur within initially motionless water. Moreover, the theoretical ratio is not complying with observation. This is qualitatively confirming the extension of de Gennes’ flows involving a rotation of the parietal layer of heavy oil flows within small pipes to all laminar flows as proposed by the associated engineers report dated 1994. This can be confirmed fully only by implementing the Hamilton’s principle to the associated engineers’ approach of kinetic angular friction within laminar flows. The associated engineers failed to obtain such a proof up to now.


The pressure is null for the value of  rc giving:


            p0 = r (  k’  - k   )     

                        r2  r4c


Instead of implementing the Hamilton’s principle, the intuitive principle of minimum energy, well known in Elasticity theory, may be used as well.



2.2   Minimum energy principle implementation


Between   t  =  - ¥  at an infinite distance and   t = tc  where the pressure is null, the kinetic energy variation is equal to the work of pressure forces for a fluid particle dm:


            d Ec     =   1  dm ( vr2   + vq2 )




            d Ec dt  =   1  dm ( k2   +k’2 )  dt

                               2          r4c    r2c 


Along a circle with r radius:    dt  =   rc  dq    


            d Ec t   =    dm 2 p  1     ( k2   +k’2

                                rc           k’      rc2 


k is the flow parameter and cannot be a condition  of the minimum energy. There shall be only one very single value for each value of K. The derivation shall be perform on k’:


            ¶(d Ec t )  =    dm 2 p  1     ( k’2   k2

                k’                rc        k’2               rc2

The minimum is obtained forr  k’ =  +  k .




Fluids mechanics equations have been issued with some fundamental hypotheses. Mainly, it is assumed that the atoms or molecules of the fluid don’t own any angular momentum. The general case shall include such an angular momentum although this is definitely not the case neither for perfect fluids nor for viscous fluids nor for superfluids.


The first point is to change the elastic impact laws. The angular momentum shall be added. The angular momentum exchange is only possible within the elasticity theory. Elastic buckles are not symmetrical. This is a result of the angular momentum. The impact zone is then buckled. The buckling combine with the flattening is preventing the fluid particles to slip on one another. Then the fluid particles have six degrees of freedom. The equipartition principle applies. The fluid mechanics equations are dramatically changes accordingly. The tangential speed law is 1/SQRT(R), instead of 1/R. Unfortunately the flow is no more irrotationnal. This is involving in fact some interesting consequences as underlined within the last paragraph.


3.1 Continuity


            div v   =  0                                                                  (1)


the relation gives the same result as for perfect fluids:


            vr  =  -  k 



This is, of course, the fluxes law.




3.2 Angular momentum theorem


The angular momentum theorem writes for a fluid volume element dv = rdq ds with ds = dr dz:


I is the inertia angular momentum of the fluid volume element related to the axis perpendicular to the flow and including the cylindrical co-ordinates origin; W is  local angular speed of the plane flow; i is the inertia angular momentum  of the fluid particles related to the axis perpendicular to the flow plane and including the gravity centre of the particles and w the revolution speed of the fluid particles around this axis. The product of those two quantities is summed up within the fluid volume element.


The main angular momentum may writes:



So that it may be written now:


Friction are nor taken into account hereafter. In this case, the whirl well flow equation hereunder becomes:


3.3 Equipartition principle.


As a consequence of energy equipartition within the fluid, the average value of angular momentum of the fluid particles is not null. Within fluids with 6 degrees of freedom, the kinetic angular energy involved by the fluid rotation shall be balanced by an energy contribution. The only possible contributors are the particles own angular momentum. The energy equipartition is equivalent to the equality:


3.2 paragraph equation becomes :


                Vq  =  -   k’      together with   Vr  =  -   k     

                                      Ör                                                        r2


The pressure is null for rc  complying with :


            p0 = rk’  - k   )     

                           rc     rc4


Although the well flow remains irrotationnal, the tangential flow, i.e. the whirl is not irrotational. Friction should be taken into account. The solution hereunder is only valid for very slow flows. The fluid speed shall remain very small compared to the quadratic mean Brownian speed.



3.4 Minimum energy principle implementation


Between t = - ¥ and t,  the kinetic energy variation is equal to the pressure force work for a fluid particle dm:


            d Ec     =     dm (   Vr2    Vq2 )



            d Ec dt  =   dm (  k2   k2 ) dt      with dt =   rc  Ö rc dq

                                         r’4c       r’c                                                k’  


            d Ec t   =    dm 2 p Ö r’ck2   +  k’2

                                k’                   r’3c           


k is the flow parameter; its value cannot be a condition of the minimum energy. It shall exist at least one solution for each value of k. Derivation shall be performed on k’:


            ¶(d Ec t )  =    dm    p  Ör’c     ( 2 k’2   k2

                k’                k’2                                            r’3c


The minimum is obtained for 


                        k     =  _______    

                                       r’c Ör’c


There is only one whirl-well flow complying with the minimum energy principle. This flow is depending upon rc, thus on how the well flow is established.


3.5 Energy transfert


Within perfect fluid, a fluid particle located at the distance r from the centre of the well has to opposite motions: the first one is linked to the overall rotation of the fluid within the whirl, the second one is a result of the tangential speed variation within the whirl. In perfect fluid, these two angular speed are equal.


w1 = Vq     =      k’                            w1 = 1Vq dr /dr    =        - k’   

           r                  r2                                      2 r          2              r2


So that fluid particles have no rotation at all. This is why the flow is irrotational. The discrepancy between the theoretical surface curve and the experimental curve shows that the conventional friction approach is not correct as it is not complying with experiment. This was the reason for proposing a new approach taking into account the angular motion of fluid particles. The very same approach deriving from the de Genness flows of heavy oil in small pipes, allows not only to explain the anomaly of laminar flows around cylinder but also the behaviour of superfluid within rotating bucket without any reference to any kind of probabilistic approach fully contradictory with fluid mechanics theory and to explain the paradoxes resulting from the Landau’s bi-fluid. This would results as well directly from the de Gennes’ flows approach. 


This rationale is only applicable when there are no angular momentum within the fluid. In the case there are such angular momentum, the angular speed of the overall flow is the double of the rotation involved by the tangential speed rotation within whirl-well flows, and I the opposite direction:


        w2 = Vq     =         k’                            w2 = 1Vq dr /dr    =        - 1     k’   

                       r                       rÖr                                       2 r        2        2  r Ör


So that there is an energy transfer needed. This is taken into account within the equations.


The energy pumped out from the Brownian angular speed energy my be calculated:

     R                               R

     ò S ½ i w22 /4  =  ò ½ (2 p r dr dz l) i  (1/4) k’2/r3    =  (p/4) l dz i k’2/R 

     ¥                        ¥

 l is the number of fluid particles in the volume element, i the inertia momentum of those particles and dz the height of the zone involved.






4 Conclusion

Full validation of the associated engineers approach, extending the de Gennes’ flows, involving fluid friction within laminar flows based upon differential angular motion friction instead of longitudinal differential motion as for solids, requires the calculation of the related Hamiltonian.


Implementation of Hamilton’s principle to fluids with internal angular momentum has been added to this paper for information only.










































La polarisation

de la couche

coronale K

du Soleil

dans le plan

de la Galaxie




of the K coronal layer

of the Sun

within the Galaxy plane










February 1997


Le présent rapport n’est couvert d’aucune protection. Son utilisation en tout ou partie ne peut générer aucun droit.

This report is public. Its use as a whole or the use of any part thereof cannot involve any subsequent right.











01 Objectifs

02 Principes







11 Le tube à diaphragmes instrumenté

12 Le viseur solaire






21 Mesures

22 Exploitation













01 Objectives

02 Principles







11 The intrumented diaphgram tube

12 The solar sight






21 Measurements

22 Analyses











On observe, dans de nombreuses circonstances, une polarisation de la lumière plus ou moins complète. La polarisation de la lumière diffusée par l’atmosphère à 90° du Soleil est fortement polarisée. On observe une légère polarisation de la lumière réfléchie par la Lune. Ce phénomène fait intervenir un passage de la lumière dans des milieux transparents, qu’il se produise une réfraction ou une réflexion totale.


Par contre, il n’en va pas de même pour la forte polarisation de la couche coronale K du Soleil et pour la polarisation partielle des étoiles. La réflexion sur des électrons ne peut en aucun cas être assimilée à une réflexion vitreuse, et la polarisation des étoiles ne fait pas intervenir de réflexion.


Des considérations sur l’application du théorème du moment cinétique ont amené à proposer une cause unique pour ces deux derniers types de polarisation et à penser que la couche coronale K du Soleil doit présenter une seconde direction de polarisation dans le plan de la galaxie, en plus de la polarisation déjà connue et globalement parallèle au plan équatorial du Soleil.


Cette seconde polarisation de la couche coronale K du Soleil a été mise en évidence le 14 décembre 1996, une semaine avant la date du passage de la direction du Soleil dans un plan parallèle au plan de la Galaxie, à l’aide d’un tube à diaphragmes instrumenté.





In many circumstances, polarization of light may be observed with a variable degree of completeness. The polarization of the light diffused by the atmosphere within an angle of 90° from the Sun is highly polarized; the light reflected by the Moon surface is slightly polarized. In both cases, the polarization is linked to a reflection or a refraction within transparent media and the related phenomena are well identified.


The situation is neither the same for the large polarization of the K coronal layer of the Sun nor for the partial polarization of the Stars. Reflection by electrons cannot be considered as a reflection on atoms, and the polarization of Stars does not involve any reflection.


From the implementation of the angular momentum theorem, it has been deducted only one explanation for these both kinds of polarization, and to think that the K coronal layer of the Sun should also be polarized in the Galaxy plane, in addition to the well known polarization approximately parallel to the equatorial plane of the Sun.


This second polarization of the K coronal layer of the Sun was found on Saturday December 14, 1997, one week before the direction of the Sun is exactly parallel to the Galaxy plane, using an instrumented diaphragm tube.








01 Objectifs


Les circonstances répertoriées de polarisation de la lumière, résultent d’un passage de la lumière dans des corps transparents. Les champs électromagnétiques sont susceptibles de provoquer ou de modifier la polarisation de la lumière à la traversée de certains milieux, mais il est essentiel de noter que les champs électromagnétiques n’ont aucun effet direct sur la lumière. Leur action sur la matière en modifie la structure et cette modification peut agir sur la lumière et en particulier sur son état de polarisation.


Il y a toutefois des exceptions : la polarisation de la couche coronale K du Soleil; il s’agit dans ce cas d’une réflexion de la lumière solaire sur les électrons de la couche K. Il n’y a donc pas de traversée d'un milieu transparent. On considère que le champ magnétique du Soleil agit directement sur les électrons pour provoquer la polarisation de la lumière. 


Un autre cas de polarisation a reçu une explication dédiée: la polarisation partielle de la lumière émise par les étoiles. Dans ce cas en effet, la polarisation résulterait de l’orientation des poussières métalliques sidérales par le champ magnétique dans les bras de la Galaxie, ce qui permettrait d’expliquer pourquoi cette polarisation est globalement parallèle au plan de la Galaxie. Il s’agirait bien du résultat d’une action structurante d’un champ électromagnétique sur la matière, mais l’explication est dédiée dans la mesure où il ne s’agit pas de corps transparents; la lumière ne peut nullement traverser des poussières métalliques.





01 Objectives


The known light polarization circumstances are linked to the behavior of light through transparent bodies. Electromagnetic fields may initiate or modify the light polarization status when going through some specific media, but it is essential to notice that electromagnetic fields have no direct effect on light. Their action on matter modifies its structure and the related change may act on the light polarization status.


Nevertheless there are exceptions. The polarization of the K coronal layer of the Sun is understood as the result of the reflection of the solar light by the electrons of the K layer. There is no transparent medium. It is considered that the electromagnetic field of the Sun acts directly on the electrons to initiate the polarization of light.


An other polarization case received also a dedicated explanation: the polarization of light coming from stars. In this case, polarization is considered as the result of an orientation of the metallic dust by the electromagnetic field of the Galaxy arms. This allows for explaining that the polarization direction is parallel to the Galaxy plane. It may be seen as an action on an electromagnetic field on mater, but the explanation is dedicated because metallic dust is not transparent.


On pense que cet ensemble structuré de particules métalliques constitue un milieu, lui-même transparent, mais ce processus de polarisation n’a jamais pu être reproduit, pas plus que le précédent d’ailleurs.


L’objet de cette note est de proposer une explication unique pour ces deux exceptions et de présenter une expérience réalisée pour mettre en évidence un cas de polarisation similaire, mais ne pouvant pas résulter de l’action d’un champ électromagnétique : la polarisation de la couche coronale K du Soleil dans le plan de la Galaxie.


La généralisation de cette explication de la polarisation de la lumière, au delà de ces trois cas, à l’ensemble des phénomènes de polarisation de la lumière, a des conséquences théoriques et expérimentales exposées dans la dernière partie.


02 Principes


La vitesse tangentielle de rotation du Soleil dans la Galaxie est du même ordre de grandeur que la vitesse képlerienne de rotation autour du Soleil à la distance de sa surface égale à une fois et demi son rayon, c'est-à-dire d’environ 250km/s. Cette coïncidence peut conduire à s’interroger sur les phénomènes qui se produisent dans cette circonstance.



It could be thought that the metallic dusts could be a transparent medium, but this had never been neither found elsewhere nor reproduced.


The subject of this report is to propose a common explanation for those two exceptions and to present an experiment performed to show a similar case of polarization which, nevertheless, can in no case be the result of the action of an electromagnetic field. This is the polarization of the K coronal layer of the Sun in the Galaxy plane.


The proposed explanation of the polarization of light may be extended to all the polarization cases. The consequences, both theoretical and experimental are presented in the last part of this report.


02 Principles


The tangential speed of the Sun within the Galaxy is within the same order of magnitude as the keplerian speed around the Sun at a distance of one and an half radius of the Sun to its surface They are 250km/s. This is a coincidence which may induce a review of the phenomena occurring in such a circumstance.



Malheureusement aucun corps ne tourne aussi près de la surface du Soleil. Mais l’existence même des couches coronales, montre qu’il a des électrons, des atomes, des molécules et des poussières, qui, même si elles ne sont pas en orbite, se trouvent dans une zone où à la fois la vitesse képlerienne de rotation autour du Soleil et la vitesse tangentielle de rotation dans la Galaxie sont très voisines.


Or il se trouve que la lumière solaire réfléchie par les électrons de la couche coronale K est fortement polarisée globalement dans un plan parallèle au plan équatorial du Soleil. En est-il de même pour cette même lumière réfléchie par ces mêmes électrons de la couche K, mais dans la direction du plan de la Galaxie?


Toutefois, il n’est possible pas de comprendre comment la vitesse peut faire apparaître une polarisation, d’autant moins que les électrons sont bien animés de la même vitesse galactique que le Soleil, mais ils ne gravitent pas autour du Soleil. Si la vitesse était la cause de la polarisation, seule existerait la polarisation galactique. Or la polarisation de la couche K, connue depuis plus d’un siècle, ne peut se rattacher à aucune grandeur, telle que le champ magnétique, ni à aucune position qui serait liée à la Galaxie. Le champ magnétique de la Galaxie, au niveau de la couche K, est extrêmement faible par rapport à celui du Soleil.


L’égalité des vitesses est la manifestation d’un autre phénomène.



Unfortunately there are no bodies turning around the Sun at a so low distance. But there are many electrons, atoms, molecules and dusts in the vicinity of the Sun within the so called coronal layers. Although they are not turning around the Sun, they are in a zone where the keplerian rotation speed is the same as the speed of the Sun around the Galaxy center.


However, the solar light reflected by the electrons of the K coronal layer of the Sun is highly polarized. This polarization is approximately parallel to the equatorial plane of the Sun. Is it the same for that same light reflected by those electrons, but in the direction of the Galaxy plane?


But how may the speed initiate polarization by its own? In addition, the electrons of the K layer are turning around the Galaxy center with the Sun, but they are not at all turning around the Sun. If the speed was the root cause of polarization, the galactic polarization would only exist. And this is not possible for the polarization of the K layer is known since many decades and it has never been found any link with the Galaxy properties. The magnetic field of the Galaxy is extremely weak compared to the Sun field.


The equality of speeds is the result of another phenomenon.




On peut définir une grandeur, pour l'instant toute théorique, mesurant le défaut potentiel de moment cinétique local par la sommation de la variation du moment cinétique d'un point matériel de masse unité, tournant autour d'un astre, qui se rapprocherait de l'astre depuis l'infini jusqu'à une distance définie. Or il se trouve que l’énergie cinétique de rotation correspondant à cette grandeur est du même ordre pour un corps tournant autour du Soleil qui se rapprocherait jusqu'à une distance de sa surface égale à une fois et demi son rayon, que pour un corps tournant autour du centre de la Galaxie qui se rapprocherait de l’infini jusqu'à la distance où se trouve le Soleil.


Le rapprochement du corps envisagé doit cependant avoir une cause physique et la compensation des moments cinétiques est nécessairement liée à cette cause. Les frottements avec les poussières et atomes de l'Espace ne peuvent être invoqués pour compenser tout à la fois l'extension et l'effondrement des systèmes galactiques ou planétaires. D'autre part, la compensation globale des moments cinétiques, apparemment satisfaisante pour l'esprit, ne peut expliquer la compensation des variations, sans qu'il soit nécessaire d'ajouter un transfert à distance à chaque instant, question aussi irritante que celle de l'action à distance de la gravitation. La conservation du moment cinétique n'est pas moins impérative que celle de la conservation de la quantité de mouvement. C’est-à-dire que le système de la gravitation doit pourvoir à la compensation des variations du moment cinétique à chaque instant et en chaque point de l'Espace indistinctement.




One may define the Angular Momentum Lack as a theoretical value obtained by integrating the angular momentum variation of a body, with a mass equal to one unit, turning around a star, while it is pushed toward the star. The kinetic energy related to this value is within the same order of magnitude both for the a body pushed from an infinite distance down to a distance of 1.5 radius of the Sun surface and for the same body pushed down to the Galaxy center down to the distance of the Sun.


Of course the motion of that body toward the Sun or toward the Galaxy center shall have a cause and this cause shall provide for the angular momentum variation clearing. Friction with sidereal matter and dust cannot be taken as a root cause both for system collapsing or extending. On another hand, the global overall clearing of angular momentum variation, although it seems to be consistent with principles, cannot explain the clearing of local variations without adding a transfer to distant points of space to be added to the distant action of gravity. The angular momentum conservation is exactly as mandatory as the linear momentum conservation. That is to say that the gravitation system shall provide simultaneously, and in every point of space for both a clearing of the linear momentum variations and a clearing of the angular momentum variations.




Dès cet instant, il faut reconnaître que c'est la totalité du moment cinétique des corps des systèmes galactiques et planétaires qui est compensée localement par le système de la gravitation quelle que soit la forme mathématique sous laquelle on l'exprime.


Maintenir une compensation globale et universelle, qui devrait, dès lors, se trouver inscrite dans le processus de formation de l'ensemble des systèmes galactiques et planétaires, conduirait à une redondance fatale. En effet lors de la formation des systèmes galactiques et planétaires, les variations de moment cinétique s'intègrent dans le temps sans que l'on puisse en arrêter la sommation jusqu’à des valeurs qui atteindront enfin exactement l'amplitude du moment cinétique actuel, supposé pourtant déjà compensé globalement.


La compensation est nécessairement locale. Elle est dès lors partout potentielle. Chaque point d’un système, est affecté d’un défaut potentiel de moment cinétique par rapport au centre du système, mesuré par la grandeur définie ci-dessus. Il s’agit toujours d’un défaut de moment cinétique et la variation de ce défaut est positive ou négative selon que le système est en extension ou en effondrement.


La gravitation a ainsi deux composantes indissociables et nécessaires. Un moyen de compensation des forces pour la conservation de la quantité de mouvement et qui se traduit par l'égalité de l'action et de la réaction et un moyen de compensation du moment cinétique pour la conservation du moment cinétique.




At this point, it shall be recognized that the total amount of the angular momentum of all the bodies belonging to a system shall be locally cleared by the gravitation system whatever is the mathematical formalism use to describe it.


A global and universal clearing would have to be operated at the very beginning of any motion of all the existing matter, and this will lead to a fatal redundancy. During the formation of galactic and planetary systems, the angular momentum variations are added to themselves without any possibility to stop the process, up to the actual value of the angular momentum, although it was assumed that this angular momentum would have been globally and universally cleared only at the very beginning.


There is no way to escape to a local and simultaneous clearing. Therefore the clearing is everywhere as potential. Every point of a system is affected with a lack of angular momentum with regard to the system center; and this lack is measured by the value defined here under. This is always a lack and the variation of this lack is either positive or negative when the system is either extending or collapsing.


Thus the gravitation has two components. One clearing mean for the angular momentum variation and one clearing mean for the linear momentum variation. The linear momentum conservation is represented by the equality of the action to the reaction.




Il faut noter au passage que la conservation de la quantité de mouvement ne peut pas davantage être globale que celle de la conservation du moment cinétique. Un raisonnement semblable au précédent conduit à considérer la nécessité d'une égalité locale de l'action et de la réaction et non pas seulement d'une égalité globale ou à distance. Le système de la gravitation doit inclure une égalité locale de l'action et de la réaction, et une compensation locale du moment cinétique, quel que soit le formalisme mathématique utilisé pour l'exprimer.


La gravitation, sous ses deux composantes ainsi reconnues, est supposée agir physiquement sur les corps de deux manières différentes. Si l’on fait l’hypothèse que ces deux composantes sont deux manifestations d’une même forme de la Nature, alors il faut également tenir compte du principe d’équipartition de l’énergie entre les degrés de liberté de cette forme unique, au nombre de six. Rien n’exclut d’en donner davantage, encore faut-il en trouver l’utilité et la justification.


En outre, cette forme ne peut disposer d’une énergie cinétique infinie. Si l’on prend comme limite 1/2 mc2, le principe d’équipartition conduit à attribuer la même limite à l’énergie cinétique de rotation, la limite totale étant naturellement mc2.


Sans qu’il soit nécessaire de faire aucune hypothèse sur la nature même de cette forme, une constatation fondamentale s’impose pour les systèmes galactiques et planétaires: l’énergie cinétique de rotation croît plus vite, en se rapprochant du centre du système, que l’énergie cinétique. La première varie avec l’inverse du cube de la distance au centre du système, la seconde avec l’inverse de cette distance seulement.



The linear momentum conservation cannot be obtained neither by a global and preliminary clearing, nor by distant actions. It is also local. The same reasoning as for the angular momentum conservation would show that a global and preliminary clearing would lead also to a fatal redundancy. The action and the reaction shall be locally equal. The gravitation system shall include both a local equality of the action and the reaction and a local clearing of the angular momentum whatever is the formalism used.


The gravitation, made of these two components, is assumed to act physically on bodies by two different ways. If it is assumed in addition, that those two components are evidence of one single form of the Nature, thus the equipartition principle shall apply between the freedom degrees of this single form. And nothing can prevent to take more or less than 6 degrees.


At last, this single form cannot have an infinite available energy. If the limit of energy attached to the linear momentum component is assumed to be 1/2 mc2, then the total amount available for both components is mc2.


Without any further assumption on the nature of that form itself, there is an immediate consequence for the galactic and planetary systems. The angular momentum grows far faster than the linear momentum while approaching the system center, when the motions are keplerian. The first is growing as the distance to the center to the minus 3, although the second is growing to the minus 1.


C’est-à-dire que l’énergie cinétique de rotation disponible dans la forme de la gravitation peut s’annuler bien avant l’énergie cinétique disponible. Les distances d’annulation respective ne peuvent se faire sans hypothèses sur la nature même de cette forme.


Cependant, les conditions de rotation des astres des systèmes doivent être modifiées bien avant que ces limites soient atteintes. Il semble que ce soit le cas dans le système solaire où une anomalie mesurable de la rotation de Mercure a été constatée. Mais c’est assurément le cas des galaxies, puisque la rotation de deux galaxies voisines n’est pas képlerienne. A fortiori la rotation des astres des galaxies n’est pas non plus képlerienne.


La diminution de l’énergie de la composante relative au moment cinétique, de la forme de la gravitation, provoque un pompage des moments cinétiques des corps placés au point considéré.


En conséquence, si le moment cinétique propre des électrons qui composent la couche K, est entièrement pompé par le défaut local lié au Soleil, il sera, de la même manière, entièrement pompé par le défaut galactique en résultat de la remarque liminaire.



The energy related to the angular momentum may be fully swallowed far before the energy relates to the linear momentum. The distances where those energies are annealed cannot be calculated without further assumptions on the gravitation form.


However, far before the energy related to the angular momentum is annealed, the rotation conditions of bodies within systems are modified. It seems that this is the case for Mercury in the Solar system. But of course it is undoubtedly the case for galaxies, as the relative rotation of two galaxies close to one another is not at all keplerian. Of course it is also the case within the galaxies themselves.


As the available energy related to the angular momentum is decreasing, the angular momentum of bodies is pumped accordingly.


As a consequence, if the angular momentum of electrons of the K layer of the Sun, perpendicular to the Solar equator, is fully pumped out by the angular momentum local lack resulting from the Sun, the angular momentum of electrons of the K layer of the Sun, perpendicular to the Galaxy plane will be also fully pumped out by the angular momentum local lack resulting from the Galaxy as a result of the preliminary remark.




Or la lumière solaire réfléchie par les électrons de la couche K est fortement polarisée. De plus cette polarisation est parallèle globalement au plan équatorial du Soleil, alors que le défaut de moment cinétique lui est perpendiculaire. Si cette polarisation est liée à ce défaut de moment cinétique des électrons, alors la même lumière solaire réfléchie par ces électrons doit aussi être polarisée dans un plan parallèle au plan de la Galaxie  puisque le défaut galactique de moment cinétique est lui-même perpendiculaire à ce plan.


Il se trouve que le plan équatorial du Soleil et le plan de la Galaxie font un angle voisin de 70°. Circonstance remarquable en cela qu'elle conduit à deux critères caractéristiques. On doit observer d'une part 4 extinctions par tour de l'analyseur, d'autre part les maxima doivent être inégaux, mais inférieurs au tiers environ de l’amplitude observée pour la seule polarisation liée au Soleil.


L’observation de la couche coronale K lors du passage du Soleil dans une direction parallèle au plan de la Galaxie, circonstance qui se produit actuellement 39 minutes avant le solstice d’hiver, a mis en évidence cette polarisation supplémentaire le 14 décembre 1996, quelques jours avant le solstice d'hiver où la couverture nuageuse n'a pas permis d'observation. L’observation effectuée en février 1997, plus de 60 jours après le solstice d’hiver, montre que seule subsiste la polarisation due au Soleil, l’effet galactique ayant disparu.


Les résultats de ces observations sont exposés au chapitre 20 après une présentation du dispositif expérimental utilisé.



But the solar light reflected by those electrons is highly polarized. Furthermore, this polarization is globally parallel to the Sun equator, the lack of angular momentum of electrons being perpendicular to the Sun equator. If the lack of angular momentum is the cause of the polarization, then that same Solar light reflected by those electrons shall be also polarized in a direction parallel to the Galaxy plane, the related lack of angular momentum being perpendicular to the Galaxy plane.


The angle between the Sun equator and the Galaxy plane is about 70°. This leads to two criteria. First, 4 extinctions shall be observed for each revolution of the analyzer, second, the maxima are not equal but both lower than a third of the normal amplitude observed for the solar polarization alone.


The measurements of the light reflected by the Sun by the coronal K layer, when the Sun is seen from the Earth in the Galaxy plane, show this supplementary polarization of the K layer. This event occurs twice a year, presently 39 minutes before the winter solstice. The measurements had been performed on the 14th December 1996, some days before the winter solstice. On the 21st, the heavy cloud cover didn’t allow for any observation. The measurements were performed again 60 days after the winter solstice. The galactic effect had disappears.


The results are detailed in chapter 20 after a presentation of the device used.




Le dispositif utilisé se compose essentiellement d’un tube à diaphragmes, équipé d’un photomultiplicateur, fixé sur une monture équatoriale.


11 Le tube à diaphragmes instrumenté


111 Partie mécanique et optique


Une boîte à diaphragmes dont le plus petit a une ouverture de 0.3 mm est fixée à une extrémité d’un tube principal en cuivre de 40 mm de diamètre, de 1 mm d’épaisseur et de 1m de long, dans l’axe du tube. Un obturateur tournant est fixé à l’extérieur.


Le tube principal est revêtu intérieurement d'une couche de peinture anti-réfléchissante et comporte dans sa partie médiane une série d'une dizaine de bourres de 1 cm de long en mousse de polyuréthane noire percées d'un orifice tubulaire de 2mm de diamètre dans l'axe du tube principal.


Un tube secondaire en aluminium, de 5 mm de diamètre, monté dans deux roulements à billes, est inséré, dans l’axe, à l’autre extrémité du tube principal. L’extrémité intérieure du tube secondaire porte un diaphragme de 0.3 mm de diamètre également. L’extrémité extérieure porte un analyseur. Un tube de 10 mm est fixé à cette extrémité du tube secondaire pour former une chicane lors de l’insertion du tube de 8 mm fixé à la face interne de la bride support du photomultiplicateur sur le tube principal et dans son axe. La face externe de la bride support du photomultiplicateur permet la fixation d’un carter de protection en plastique.






The device used is essentially made of a tube with diaphragms fitted with a photomultiplier, attached to an equatorial mount.


11 The instrumented diaphragm tube


111 Mechanical and optical part


A diaphragm box with the smallest diaphragm diameter not greater than 0.3 mm, is fitted to one end of a copper main tube 1 mm thick, 1 m long and 40 cm diameter, in the axis of the tube. A rotating shutter is attached outside the tube.


The main tube is internally coated with an antireflection painting and includes, near its middle, about ten bored black wads 1cm long made of polyurethan. The bores are 2 mm diameter in the axis of the main tube.


A secondary aluminium tube 5 mm diameter mounted on rolling bears, is fitted inside the main tube. A diaphragm, also 0.3 mm diameter, is fixed to the internal end of the secundary tube. The external end bears an analyzer. A 10 mm copper tube is welded at this end of the tube in order to form a chicane whith the 8 mm diameter tube welded to the internal face of the photomultiplier support flange. The external face of that flange allows for fitting a plastic protection tube.



Le tube secondaire est entraîné en rotation par une courroie reliée à un moteur par l’intermédiaire d’un volant d’inertie. Le volant et le moteur sont fixés à l’extérieur du tube principal. Les deux traversées de la courroie sont protégées en sorte que l’entrée de lumière soit limitée au minimum. La chicane décrite ci-dessus complète la protection.


L'ouverture du tube à diaphragmes est de 2.5'.



Un viseur optique réticulé, équipé d’un filtre solaire est fixé au tube principal.






                                               Schéma du tube à diaphragmes instrumenté




                                                                       moteur / motor




                                                                     Photomultiplicateur / Photomultiplier



                                               Principle of the instrumented diaphragm tube





The secondary tube is actuated by a motor fitted outside the main tube. A fly wheel is used both for rotation smoothing and speed reduction. The crossings of the strap through the main tube are properly protected to reduce the path for light to a minimum. Any remaining light which would enter the tiny remaining gaps is stopped by the chicane described here above.


The opening of the diaphragm tube is no more than 2.5'.


An optical sight with a reticle is attached ouside the main tube.






112 Partie électrique.


Un boîtier de connexion et de contrôle est fixé au tube principal. Il comporte un connecteur SUBD9M relié aux câbles d’alimentation et de contrôle du photomultiplicateur, une prise BNC relié au câble de sortie du photomultiplicateur, un potentiomètre et un multimètre digital pour le réglage de la tension de contrôle. Le boîtier est relié aux alimentations  12 V et à la masse.


Ce boîtier comporte également un potentiomètre de réglage de la vitesse du moteur et un connecteur SUBD9M relié aux cables d’alimentations du moteur lui-même et du compte-tours en 9 V et 1.5 V respectivement. Les moto-réducteurs utilisés pour les mesures tournent entre 6 et 24 tours par minute ce qui correspond, compte tenu du volant d’inertie qui joue également le rôle de réducteur par son mode d’entraînement, à une vitesse du tube secondaire porte analyseur de 0.75 tour par minute à 3 tours par minute.


Le compte-tours consiste en deux plaques souples isolées en cuivre fixées à l’intérieur du tube principal. Le courant est établi par le passage des plaques au contact d’un fil soudé longitudinalement au tube de la chicane fixé au tube secondaire. Un bruiteur électronique fixé au tube principal est actionné par le compte tours.


Les alimentations 12 V sont régulées et stabilisées avec une ondulation crête à crête inférieure à 3 mV.


Les autres alimentations sont des piles du commerce.





112 Electrical part


A connecting and control box is fixed to the main tube. It includes a SUBD9M connector linked to the power supply and control unit of the photomultiplier and a BNC connector linked to the output of the photomultiplier. It includes also a potentiometer and a digital voltmeter for the setting of the control voltage. The box is connected to the ground and to the bipolar power supply.


The box includes also a potentiometer for the setting of the motor speed and a connector SUBD9M also for connection to the power supplies of the motor, the multimeter and the revolution counter (9 V DC, 9 V DC, 3 V DC). The electrical DC motors include reducers. Their speeds are within the range 6 to 24 rpm. The rotation speed of the analyzer, taking into account the flywheel reduction factor, is within the range of 0.75 to 3 rpm.


The revolution counter is made of two thin copper strips bolted inside the main tube by insulated bolts. The circuit is closed by a copper transversal wire welded to the external tube of the chicane. An electronic buzzer is actuated by the revolution counter.


The 12 V power supplies are regulated and stabilized so that the peak to peak ripple  is below 3 mV.


The other power supplies are batteries. 



113 Partie photométrique


Un photomultiplicateur est fixé à la bride mentionnée ci-dessus. Les caractéristiques essentielles du photomultiplicateur sont données dans le tableau ci-après.


114 Partie acquisition


La prise BNC du boîtier de connexion et de contrôle et la sortie du compte-tours peuvent être reliées à un module d’acquisition par un connecteur SUBD25M. Le module d’acquisition est lui-même relié à la sortie parallèle d’un ordinateur portable. Un adaptateur d’impédance à amplificateur opérationnel à transistors à effet de champ peut être inséré entre le module d’acquisition et le connecteur SUBD25M.


Le logiciel d’acquisition, fourni avec le module, permet de reporter les valeurs obtenues sur excel.


Un connecteur SUBD25F permet de remplacer le dispositif d’acquisition par des voltmètres d’une sensibilité inférieure au mV.


12 Le viseur solaire


Le viseur solaire est conçu pour déclencher une alarme de proximité de la surface du Soleil. Le signal d'alarme peut être envoyé au dispositif d'acquisition dont le logiciel peut actionner des voyants d'écran ou le haut-parleur de l'ordinateur.



113 Photometric part


A photomultiplier is fixed by four 2mm screws to the flange mentioned here above. The main characteristics of the photomultiplier are indicated by the table here after.



114 Acquisition part


The BNC connector of the connector and control box and the output of the revolution counter may be connected to an acquisition module through a SUBD25M connector. The acquisition module is plugged in a parallel port of a laptop computer. An impedance adapter with field effect transistors may be placed between the acquisition module and the SUBD25M connector. The acquisition software, supplied with the module, allows for transferring data to EXCEL.


A SUBD25F connector linked to multimeters may be plugged instead of the module. The sensitivity of the multimeters is lower than 1 mV.


12 The solar sight

 The solar sight is intended for preventing the photomultiplier to be placed toward the Sun disk. The alarm may be sent to the acquisition module provided with software features such as screen lights or signals for the computer loud speaker or buzzer.



Le viseur solaire est fixé à l'extérieur du tube à diaphragmes, et dans son axe. Il est constitué d'un tube de 15 mm de diamètre et de 20 cm de long. Dix diaphragmes de 1mm de diamètre sont fixés à intervalles réguliers à l'intérieur du tube. L'ouverture est de 30', soit le diamètre apparent du Soleil.


Une photodiode est fixée à l'extrémité du viseur dans un tube coulissant facilement extractible, en sorte que le viseur puisse être utilisé directement à l'oeil. Le signal de la photodiode est envoyé sur un amplificateur opérationnel à correction d'offset. Le dispositif a été conçu pour que le gain soit de 100. Le signal amplifié est envoyé sur un voltmètre fixé au tube, dont la sensibilité est de 10 mV et sur deux amplificateurs opérationnels montés en comparateurs délivrant un signal continu pour des valeurs du signal d'entrée respectivement inférieur et supérieur à leur tension de référence préréglée. La sortie de chaque comparateurs alimente une diode électroluminescente respectivement rouge et verte. La tension de référence correspond au signal maximum donné par la photodiode du viseur solaire placé dans la direction du Soleil.


A l'issue des réglages de parallélisme entre le tube à diaphragmes et le viseur solaire un décalage angulaire de 15' est donné au viseur solaire dans le sens des aiguilles d'une montre, grâce à une vis de réglage insérée dans la fixation du viseur au tube à diaphragmes.


The solar sight is attached to the main tube and parallel to its axis. It is made of a copper tube 15 mm diameter and 20 cm long.10 diaphragms 1 mm diameter are fixed inside the tube. The opening is 30', that is to say the Solar apparent diameter.


A photodiode is fitted at one end of the tube within a grooving tube. This tube may be removed easily so that the sight can be used directly. The output signal of the photodiode is amplified by a FET operational amplifier mounted with a 100 gain. The amplified signal is then sent to two comparators actuating respectively a red LED and a green LED. The set value of the comparators is the amplified signal delivered by the photodiode when placed towards the Sun.


When all settings are done, the solar sight axis is turned by a screw provided in its support by 15' backward from the instrumented diaphragm tube axis.











Manufacturer   :           HAMAMATSU

Module series  :           H5784

Serial number   :           840-331

Sensitivity         :           127.0E+6 V/Lm control voltage 0.8V (1)

Time resp.        :           0.65 ns

Spectral resp.   :           300 to 650 nm


The module includes a voltage regulator, a high voltage Cockford-Walton bridge power supply and a bipolar (min 11.5V, max 15.5V) amplifier delivering a voltage signal (conversion factor 1V/mA).



note 1: Taking into account the nominal response curve, the sensitivity is 16 E+6 V/Lm for control voltage 0.6V











21 Mesures


211 Mesures préliminaires


a) protections


Obturateur fermé, moteur en route, tube dans l'axe du Soleil, le signal du photomultiplicateur ne dépasse pas l’offset, à la valeur nominale de contrôle 0.8 V.


b) vérifications


Des mesures ont été réalisées à l'aide d'une lampe ordinaire à fil de tungstène et à halogène, à des distances telles que le signal corresponde à la valeur calculée pour la couche K.


Les tensions enregistrées par l'ordinateur présentent des oscillations très importantes. La polarisation provoquée de la lumière émise a pu être observée sur les courbes obtenues malgré ces oscillations. Toutefois, elles rendraient entièrement impossible la détection de variations d'éclairement quatre fois plus faible. Ce phénomène a été attribué d'abord à un problème d'impédance et un adaptateur a été réalisé pour y remédier, mais sans succès. Le constructeur devait d'ailleurs indiquer entre temps que l'impédance de sortie du photomultiplicateur n'est que de 1 kW, valeur qui exclut tout problème de ce genre.






21 Measurements


211 Preliminary verifications


a) protections


The photomultiplier offset value is obtained for a voltage control value of 0.8 V, when the shutter is closed and the tube is turned toward the center of the Sun.


b) Other verifications


Measurements had been performed with tungsten wires and halogen lamps. The distance to the lamps was such as to obtain a signal similar to the calculated value for the K layer.


The voltage values registered by the computer are oscillating within an high amplitude. The light observed through a polarizer fixed to one of the holes of the rotating shutter gave registered values showing both maxima and minima per revolution of the analyser, but the results show the expected values for the K layer would be unusable when the amplitude will be reduced by a third. The first cause found was a wrong balance of the impedances. An impedance adaptator had been made with a FET operational amplifier, but without results. This could not be the cause of the failure as the impedance value of the photomultiplier finally obtained from the manufacturer is only 1 kW. With such a value, there cannot be any impedance problem. 


Le plus probable est que la lecture du signal par le convertisseur analogique-digital est beaucoup trop rapide. Et comme le logiciel fourni ne permet pas de descendre en-dessous d'une mesure tous les dixièmes de seconde, il n'y pas de possibilité de traitement statistique. L'enregistrement par l’ordinateur du bleu du ciel est totalement inexploitable. La solution la plus simple devrait consister à placer un amplificateur opérationnel monté en intégrateur avant le digitaliseur. Toutefois, à partir du 7 décembre 1996, il a été décidé d'interrompre les tentatives d'amélioration du dispositif d'acquisition afin de tenter des mesures de la couche K au solstice d'hiver. La suite des mesures a été réalisée au voltmètre.


Le bleu du ciel donne une tension maximale de sortie du photomultiplicateur de 25 à 30 mV à 90° de la direction du Soleil. L'ordre de grandeur de cette valeur est conforme aux calculs qui ont conduit au choix du photomultiplicateur. La polarisation atteint plus de 80%. La légère montée de la courbe obtenue provient du mouvement de la Terre, le moteur d'ascension droite n'ayant pas été mis en route lors de cette mesure.


Polarisation du bleu du ciel: signal photomultiplicateur en mV, rotation analyseur en ° en abscisse.

Sky blue day light polarization. y-axis Photomultiplier signal in mV, x-axis analyser revolution in °


The cause of the problem may be more probably related to the very fast reading of the signal by the AD converter. Unfortunately the software supplied with the acquisition device is limited to 1 measurements every 0.1 second so that there are not enough values for a statistical treatment. The values registered for the polarization of the blue day light of the sky are fully unusable. The corrective action should be to insert an operational amplifier fitted with capacitors as an integrator before the acquisition module. Nevertheless it was too late and on the 7th of December 1996, it was decided not to try to improve the acquisition mean any more and to use a multimeter instead, so that the winter solstice measurements may be performed.


The curve here above is related to the sky blue day light. The maximum voltage value of the photomultiplier signal with a control voltage to 0.8 V is about 25 to 30 mV. The order of magnitude of these values are complying with the value calculated and used to choose the photomultiplier. The slight ascending slope of the curve is a result of the Earth rotation as the right ascension motor of the equatorial mount had not been switched on.




L'absence de nuage le 7 décembre 1996, a été mise à profit pour vérifier le viseur solaire. Cependant, l’impossibilité d’utiliser le dispositif d’acquisition, et en particulier la nécessité de lire les valeurs de la tension du signal délivré par le photomultiplicateur, n’ont pas permis d’utiliser le viseur solaire. D'autant moins, d'ailleurs, que d'autres incidents allaient limiter son utilisation au règlage initial de chaque série de mesures. Le viseur a été remis dans l’axe du tube principal dans ce but.


212 Mesures de la polarisation de la couche K


Une première mesure du signal donné par la couche K a pu être effectuée ce même jour. La tension est montée à 1400 mV à une distance de la surface du Soleil d'environ 1/5 de rayon, correspondant à deux fois l'ouverture du tube à diaphragmes. Cette valeur est dix fois la valeur attendue, calculée d'après les données connues de l'éclairement solaire: 1E+5 lux, la couronne ayant un éclairement 1E-5 fois plus faible, encore faut-il penser que c'est là une donnée valable dans le plan de l'équateur au moment optimal du cycle. Or, nous sommes cette année au minimum du cycle solaire. De plus, par manque de temps et d'expérience, on s'est contenté de viser au début de chaque cycle de mesures le point le plus à l'Est, et non un point dans le prolongement de l'équateur solaire.





As there were no clouds on the 7th of December 1996, a verification of the solar sight has been performed. However, as it was not possible to use the computer data acquisition system, and mainly as it was necessary to read the photomultiplier multimeter output, the solar sight has not been used as intended. In addition further problems occurred so that the solar sight was only use for the initial verification of the tube positionning before approaching the Sun surface. It has been set aligned with the main tube.


212 K Layer polarization measurements


A first measure of the K layer signal was performed also on the 7th. The multimeter output voltage value reached 1400 mV at a distance of the Sun surface not greater than a fifth of its radius, equivalent to two openings of the diaphragm tube. This is ten times the expected value calculated from the following data: Sun disk : 1E+5 lux, coronal layer 1E-5 the Sun disk value. But these values are probably valid for the upper part of the solar cycle and near the equator of the Sun. We are presently in the lower part of the solar cycle. Moreover to save time, and also by lack of experience, the tube was trained toward the most eastern part of the Sun and not toward the equatorial plane.




Cette valeur dix fois plus élevée que prévu, ne peut résulter que de la diffraction et des réflexions dans le tube. Ceci devait d'ailleurs être confirmé le samedi suivant, au moment où le Soleil fut caché progressivement par une cheminée, puisque le signal s'est mis à baisser beaucoup plus rapidement que du fait du seul éloignement du Soleil résultant de la rotation de la Terre. La distance du tube à la cheminée est en effet parfaitement négligeable par rapport à l'épaisseur de la couche d'air pollué traversée ; la diminution de la diffusion sur une si courte distance ne peut atteindre une telle proportion.


L'amélioration du tube nécessite son démontage. Il a été décidé de laisser les choses en l'état pour tenter malgré tout la mesure d'hiver.


La suite de la journée a été consacrée à une initiation au fonctionnement de la monture équatoriale. L'enclenchement du moteur d'ascension droite provoque un déplacement du tube de plusieurs minutes. Un astronome amateur n'aurait certainement pas eu de peine soit à éviter ce problème, soit à en tenir compte dans le positionnement du tube avant enclenchement.


Le Soleil a été caché du 8 au 13 décembre. Un vent d'Ouest a dégagé le ciel, et le matin du 14 décembre 1996 un léger vent d'Est a séché l'air. Il est probable que les conditions ont été idéales pendant les deux heures de la matinée où les mesures sont possibles, compte tenu de la situation du poste d'observation, malgré la présence du boulevard périphérique de Paris en plein Sud, à trois cent mètres et les cheminées de la centrale thermique d'Issy à peine au delà.



This value is as large as ten times the calculated value. This can only be the result of diffraction and reflections inside the tube. This was confirmed the week after when the Sun went hidden by the chimney. The signal starts decreasing far more faster than the normal rate due to the revolution of the Earth. The distance between the tube and the chimney is not significant compared with the thickness of polluted air beyond the chimney ; the decrease of the diffusion cannot be so high for a so short distance.


The diaphragm tube shall be dismantled for any improvement, so that it was decided to leave it as it was in order to be able to perform the winter measurement.


The rest of the days was devoted to an initiation to the use of the equatorial mount. When the right ascension motor is engaged, the tube turns by some minutes. This should not have been a problem even for an amateur either to avoid the problem or to take into account the change in the initial positioning.


The Sun remains hidden from the 8th to the 13th of December. A strong West wind cleans the sky and on the 14th in the morning a slight East breeze made it dry. Probably such circumstances were the best as possible during some hours, despite the high level of the pollution in this area. The Paris orbital is not farther than 300 m and the Issy power generation plant is just in the background. In addition, the measurements are only possible during the two first hours in the morning from the location where they were performed.




Dès midi, des filaments nuageux apparurent. Une heure plus tard le signal devenait erratique et atteignait 5000mV dans un nuage proche du Soleil. Ces conditions ne se retrouveront pas avant le mois de février 1997. Ce sont donc les mesures du 14 décembre 1996 qui sont présentées.


Un manque total d'expérience en observation astronomique, autant sans doute que la tension provoquée par la crainte de détruire le photomultiplicateur par une fausse manoeuvre (au début de chaque série de mesure, le tube à diaphragme est pointé à moins de 2 fois son ouverture de la surface du Soleil, le moindre faux mouvement aurait provoqué la destruction du photomultiplicateur), n'ont pas permis de comprendre immédiatement que le moteur d'ascension droite, insuffisamment bloqué sur son axe, pour être enclenché le plus délicatement possible, allait à chaque reprise des mesures, tourner autour de son axe et s'écarter de la roue dentée de l'axe d'ascension droite au lieu de la faire tourner. C'est donc le défilement à l'aval du Soleil, de la lumière solaire réfléchie qui a été mesuré.


A posteriori, cet incident a peut-être été une chance inespérée. Les mesures effectuées en février avec le moteur d’ascension droite sont difficilement exploitables. Toutefois, les mesures de février sans moteur d’ascension droite ont été effectuées en priorité pour permettre les comparaisons avec les mesures de décembre, en sorte que les mesures plus tardives avec le moteur ont été réalisées alors que de nombreux nuages s’étaient déjà développés.





When the Sun came back after the chimney, mare’s tail clouds appears, just after noon, and the photomultiplier signal went erratic. A tension as large as 5000 mV was obtain on a cloud close to the Sun and the shutter was immediately turned closed. So fine conditions were not found before the end of February, so that the measurements performed on the 14th December 1996 are brought up.


A complete lack of experience added to the fear to destroy the photomultiplier in case of a wrong operation ( at the beginning of each measurement series, the diaphragm tube is trained at a distance of the Sun surface as low as twice the tube opening, the slightest unexpected move should have destroy the photomultiplier), don’t allow for understanding immediately that the right ascension motor was not correctly engaged. The motor had been slightly tightened on its axes to allow for a smooth move. But in fact it was insufficiently tightened and it turned around its axis instead of turning the gear of the right ascension. The measurements are thus related to the passage of the reflected light, after the Sun, while the earth is turning.


This incident was probably a good luck. The curves obtained from the measures performed end of February, with the right ascension motor switched on, are even worst. However, these measures have been performed after the measures with the motor off, in order to allow for comparison with the curves obtained in December. The bad results, with the right ascension motor on, may probably result from clouds appearing at that time.




Les huit premiers essais ont été réalisés en prenant directement note des valeurs lues. Le rythme d'écriture ne dépassait pas 1 par seconde. Pour augmenter le nombre de points de mesure, le moteur d'entraînement de l'analyseur a été changé. C'est seulement à cet instant déjà tardif que l'idée d'enregistrement sur magnétophone est venue à l'esprit. Les 3 dernières séries de mesures ont pu être enregistrées avant que le Soleil ne soit caché par une cheminée. La troisième de ces séries à été perturbée très tôt par la cheminée et les résultats sont inexploitables.


La densité électronique de la couche K diminuant avec la distance à sa surface, on s’est efforcé de commencer à viser un point aussi proche de la surface du Soleil ne donnant pas un signal du photomultiplicateur supérieur à 1500mV. La lunette de visée permet d'estimer que la distance correspondante à la surface du Soleil n'excède pas 1/5 de rayon solaire. L'enregistrement est arrêté lorsque la variation est inférieure à 1 mV.


22 Exploitation


Il s'en faut de beaucoup que l'exploitation des courbes soit aisée. Le phénomène cherché ne représente que 1% de la tension maximale mesurée au début de chaque série. Les séries de mesures enregistrées présentent des variations brutales de plusieurs dizaines de mV. Les 8 séries prises par écrit, effectuées plus d’une heure avant les autres, ne présentent pas ce défaut, probablement dû à des formations brumeuses augmentant la diffusion.


Les courbes obtenues ont été corrigées d'une décroissance d'éclairement inversement proportionnelle au carré de la distance à la surface du Soleil, mesurée par la position de l'analyseur.


The eight first tests were performed while the signal values were directly registered in writing. No more than 1 value per second was registered. In order to increase the number of values, the analyzer motor was changed for a slower one. But at that very late moment, the idea to register the value with a tape recorder went to mind. The three last measurement series were recorded before the Sun went hidden by a chimney. The third one was affected very early by the chimney and it is not usable.


As the electronic density of the K layer is decreasing with the distance to the Sun, the series begin as close as possible to the Sun surface at a point where the signal is as high as 1500 mV down to a point where the signal does not change by more than 1 mV. The optical sight allows to estimate that the initial distance to the Sun surface was not exceeding 1/5 Sun radius.


22 Analyses


The analyses of the results is not easy. The effect searched is not larger than 1% of the maximum voltage at the beginning of each series. Moreover, for the recorded series, fierce voltage variations occurred; they may be several time 10 mV. As the 8 series registered in writing are not affected by such variations, it is assumed that they result from misty cloud development increasing the diffusion.


The curves obtained have been corrected by signal voltage decrease proportional to the distance to the Sun surface to the minus 2. The distance is measured by the position of the analyzer.

Pour les courbes enregistrées, cette correction a été faite par zone de décroissance moyenne régulière entre les variations brutales mentionnées ci-dessus; seules les parties des courbes comprises dans un intervalle intérieur à ces zones ont été exploitées. Par chance, une partie des mesures de la première série enregistrée présente une zone couvrant une fois et demie la rotation complète de l'analyseur. La situation est moins favorable pour la seconde série; mais la zone allant de RS à 2RS de la surface du Soleil est exploitable. Dans tous les cas, la chute très rapide du signal, dans la zone comprise entre la surface du Soleil et une distance de 1 rayon solaire, ne permet pas l’exploitation des valeurs relevées. Pour cette raison, seules les séries prises par écrit numérotées 1, 5, et 6 ont pu être utilisées soit parce qu’elles couvrent deux tours de l’analyseur soit parcequ’elles ont commencé assez loin du Soleil; les autres relevés, ayant été interrompu trop tôt, ne sont pas utilisables.


Il faut ajouter que la rotation de l'analyseur n'était pas parfaite en raison de l'élasticité de la courroie, non prévue pour une vitesse aussi faible. Cependant la révolution complète est un paramètre incontestable, car constaté indépendamment de la vitesse de rotation.


Bien que la période soit la plus basse du cycle solaire, bien que la saison soit la plus défavorable, bien que la pollution hivernale du site d'observation soit parmi les pires, bien que de nombreux problèmes matériels aient largement dégradé les conditions des mesures, bien que l'opérateur manquât totalement d'expérience pratique dans tous les domaines concernés, mais grâce sans doute à une matinée exceptionnelle, et grâce aussi à la puissance du photomultiplicateur et à son excellente linéarité, l’ensemble des courbes exploitables obtenues ne laissent aucun doute.



For recorded series, this correction is implemented for each zone where the light decreasing is sufficiently regular so that the fierce voltage variations cannot affect the interpretation. Only these zones have been used. By chance one zone of the first recorded measurement series is longer than one and an half revolution of the analyzer. The situation is not so good for the second series where only the zone included between the distance RS and 2RS to the Sun surface has been used. In all cases, the decrease of the signal between the Sun surface and a distance of 1 radius is so fast that the measurements cannot be used. For this reason, the series registered in writing N° 1, 5 and 6 only have been used, either because they involve two revolutions of the analyzer or because they begin far enough from the Sun; the other series cannot be used.


It shall be added that the rotation of the analyzer is not regular as the stripe was not intended for a so low rotation speed. Nevertheless the full revolution of the analyzer is not doubtful as it was measured by an independent way.


Although the period was the lowest of the Sun cycle, although the season was the worst, although the winter pollution of the site was among the worst, although many technical problems lowered deeply the observation conditions, although the operator recognizes a complete lack of practical experience in all the technical fields involved, but thank to an exceptional weather and to the power and linearity of the photomultiplier, all the curves obtained leave no room for any doubt.



Entre des distances de 1 à 3 rayons solaires de la surface du Soleil:


- l'amplitude maximale des variations de l'éclairement, mesurée pour chaque demi-période, est inférieure à 20mV au lieu de 40mV. (Un premier calcul effectué à partir des valeurs connues et de l’ouverture du tube à diaphragmes, donnait 65mV pour une tension de contrôle de 0.8V, valeur qui a été portée à 40mV, pour une tension de contrôle de 0.6V, compte tenu du signal réellement obtenu pour le bleu du ciel).


- des maxima et minima d'éclairement se retrouvent le plus souvent tous les 90°, c'est-à-dire 4 fois par tour et certainement pas 2 fois seulement.
















distance to the Sun surface

distance à la surface du Soleil



         RS                                                                  2RS                                           3RS




                                                               sortie PMC en mV, rotation analyseur en degré en abscisse

                                                                      PMT signal mV , anlyzer rotation in x-axis in °

                                                                   1ère série de mesures enregistrée(14 décembre 1996 11:00)

                                                                    first recorded measurement series (December 14th, 1996; 11:00)









Between 1 and 3 radius to the surface of the Sun:


- the lighting variation maximum amplitude, measured for each half period is lower than 20 mV instead of 40 mV. (A first calculation, done with the values given by books and with the diaphragm tube opening, lead to 65mV for 0.8V control voltage. This value was increased up to 40mV for 0.6V control voltage taking into account the effective signal given by the blue sky light).


- Light maxima and minima are observed the most often every 90°, that is to say 4 times per revolution, and in no case two times only.




Le 22 février 1997, des conditions semblables à celles du 14 décembre 1996 se sont présentées, cependant un fond de brume subsistait et des nuages épars perturbèrent plusieurs séries de mesure. On a reproduit ici la première, réalisée comme le 14 décembre sans moteur d’ascension droite. La mesure commence à plus d’un rayon de la surface du Soleil. Avec une tension de contrôle de 0.6V, comme en décembre, la première valeur, à cette distance, peut dépasser 1400mV. On notera que les essais de vérification sans analyseur, effectués entre temps, ont nécessité son enlèvement et qu’il n’a pas été recollé dans la même position, en sorte que les maxima ne se produisent pas aux mêmes angles que pour les mesures du 14 décembre. Toutefois toutes les courbes obtenues avec les mesures du 22 février montre des maxima aux mêmes angles. .


On observe la polarisation normale de la couche K par le Soleil. La partie gauche de cette courbe semble montrer que l’effet galactique n’a pas entièrement disparu. Les autres courbes obtenues ne descendent pas aussi près de la surface du Soleil et ne présentent pas ce maximum galactique. L’amplitude, à distance égale de la surface du Soleil, est pratiquement le double de celle constatée en décembre, mais une partie de l’augmentation résulte certainement de l’augmentation de l’éclairement.



distance to the Sun surface     distance à la surface du Soleil

  RS                                          2RS                                              3RS             

sortie PMC en mV, rotation analyseur en degré en abscisse           PMT signal mV , anlyzer rotation in x-axis in °

      1 ére série de mesures (22 février 1997 10:45)                                  first measurement series (February 22th, 1996; 10:45)



Similar conditions as on the 14th December 1996 were found on the 22nd February 1997. Nevertheless the weather was misty and clouds disturbed several series of measurements. The first curve was obtained with the right ascension motor off. The first measurement is performed at a distance of the Sun surface not smaller than one radius. The first value is 1400mV for a control voltage of 0.6V as in December. The analyser has been removed in order to perform the verification without analyser and is has not been sticked back exactly in the same position, so that the angle of the maxima cannot be compared with the curve obtained on the 14th of December. Nevertheless, all the curves obtained on the 22nd of February show the maxima for the same angles.


The normal polarization of the K layer by the Sun appears. The left part of the curve shows that the Galactic effect seems not to have fully disappeared. But this is not the case for greater distances from the Sun surface as shown also by the other curves obtained from which none is going so close to the Sun surface as this one. The amplitude is twice the one measured in December, nevertheless a part of the increase is certainly resulting from the increase of the lighting.





31 La polarisation de la lumière


Les deux défauts de moment cinétique des électrons de la couche K, liés donc l’un à la Galaxie, l’autre au Soleil, entraînent ainsi la polarisation de la lumière qu’ils réfléchissent, dans les deux directions transversales perpendiculaires aux directions de ces défauts de moment cinétique.


Le fait que la polarisation de la lumière correspond elle-même à une lacune dans la répartition des moments cinétiques, que la lumière doit donc transporter, résulte de l’unicité du phénomène. La polarisation de la lumière n’est qu’un seul phénomène en ce sens que les polariseurs et les analyseurs sont interchangeables. L’interchangeabilité n’est pas toujours facilement réalisable. Ainsi il serait difficile d’utiliser la polarisation de la couche K comme analyseur d’une lumière préalablement polarisée, car il faudrait soit une source polarisée de la même puissance que le Soleil, soit polariser toute la lumière émise. Mais on verra plus loin que l’on peut concevoir une expérience équivalente. En tout état de cause, aucune expérience à ce jour ne montre le contraire. De plus, la proportion de lumière polarisée réfléchie, dans la polarisation vitreuse, est telle qu’il est exclu que les électrons soient les seuls agents de la réflexion et donc de la polarisation. En conséquence la polarisation n’est pas une interaction de la lumière avec les électrons. L’unicité du phénomène entraîne qu’il est impossible que la polarisation de la lumière soit d’origine électromagnétique.




31 Polarization of light


Both electron angular momentum defects, one linked to the Sun, the other one linked to the Galaxy, produce as a consequence the polarization of light reflected by electrons of the K layer, in the directions perpendicular to the angular momentum defect directions.


The polarization of light is in fact a lack within the angular momentum distribution, carried along by the light, as a result of the uniqueness of the phenomenon. Polarization of light is one single phenomenon, that is to say that polarizer and analyzer may be exchanged. The exchange is not always easy. For instance it is difficult to imagine how the K layer polarization could be use as an analyzer for the polarized source should be as bright as the Sun or all the light or the Sun should be first polarized. But a similar experience can be imagined as it will be shown later in this report. Any way there are no experience showing that the polarization is not a single phenomenon. Moreover, the part of the polarized light by the vitreous reflection is so high that electrons cannot be the only agents of polarization. As a consequence, the polarization of light is not an interaction between light and electrons. The uniqueness of this phenomenon makes it impossible that the polarization of light could have an electromagnetic nature.




La polarisation est en effet parfaitement indépendante, non seulement des champs électromagnétiques comme le montre la polarisation de la couche coronale K du Soleil dans le plan de la Galaxie, mais également indépendante des charges électriques comme on vient de le montrer.


La polarisation correspond à une lacune dans la répartition des moments cinétiques transmis par la lumière. Chaque élément qui compose un pinceau lumineux transporte un moment cinétique de direction définie, perpendiculaire à sa direction de propagation. Il n’y a donc pas d’éléments de ce pinceau transportant un moment cinétique perpendiculaire à la direction de polarisation, choisie historiquement comme la direction d’éclairement maximal. En fait, les choses sont un peu plus complexes: c’est la composante du moment cinétique de chacun des élements du pinceau lumineux qui manque dans la direction perpendiculaire à la direction de polarisation comme le montre la variation, en général elliptique, de l’éclairement derrière l’analyseur.


C’est ainsi que la lumière qui nous parvient des étoiles de la Galaxie, principalement situées à proximité du plan de la Galaxie, est partiellement polarisée par pompage progressif, au cours de sa propagation, par la lacune Galactique de moment cinétique, perpendiculaire au plan de la Galaxie.


Il doit en être de même pour la lumière qui nous parvient des autres galaxies et qui, soit se trouvent à proximité du plan de la Galaxie, soit sont observées dans leur plan principal.




Polarization of light is fully independent from any electromagnetic field, as shown by the K layer polarization in the Galaxy plane, but, in addition, it is fully independent from the electric charges as it has just been said.


Polarization is related to an angular momentum distribution lack carried along by light. Each unit of a pencil of light carries along an angular momentum perpendicular to the propagation direction, in a fully defined direction. There is not any unit of this pencil of light carrying along an angular momentum perpendicular to the polarization direction. This polarization direction has been historically chosen as the maximum lighting direction. In fact, this is more intricate. The angular momentum component of each unit of the pencil of light is missing in the direction perpendicular to the polarization direction as shown by the elliptic distribution of the lighting after the analyzer.


For the very same reasons, the light coming from stars, mainly located in the vicinity of the Galaxy plane, is partially polarized by the progressive pumping of the angular momentum component perpendicular to the Galaxy plane, of the light units by the Galactic angular momentum lack.


The same pumping occurs for both the galaxies located near the Galaxy plane and the galaxies observed within their main plane.



La conséquence fondamentale de cette nouvelle approche de la polarisation est de remettre en cause le postulat de Maxwell. Si l’idée que la lumière et les ondes dites électromagnétiques sont de même nature fut proprement une intuition géniale, l’hypothèse que ces ondes sont en elles-mêmes de nature électromagnétique apparaît, avec le recul, tout à la fois comme arbitraire et redondante. Il faut reconnaître qu’il n’y avait guère de solution à l’époque. On était alors près d’un demi siècle avant que la structure de l’atome ait commencé à être envisagée sous la forme que nous lui donnons encore.

L’hypothèse est arbitraire, parce qu’elle attribue au phénomène une nature électromagnétique, sur ce simple constat que les champs semblaient jouer un rôle dans son émission et dans sa réception dans les domaines des fréquences suffisamment faibles par rapport à la lumière. Il faut toutefois reconnaître que l’hypothèse n’a rien d’absurde, elle est seulement arbitraire. Mais le plus grave est la redondance. Elle n’est apparue que récemment. Le déplacement des électrons, provoqué par le passage d’une onde électromagnétique, crée un champ électromagnétique qui suffit pour expliquer les phénomènes observés. Il n’est nullement nécessaire de supposer que les ondes sont en plus électromagnétiques en elles-mêmes. Si une onde fait déplacer mécaniquement une charge électrique, il en résulte un champ. Il n’est nullement nécessaire de supposer que l’onde soit un champ par elle-même.


De l’arbitraire, de la redondance, et enfin de l’existence de la polarisation indépendamment de tout champ électromagnétique et des charges électriques, il résulte que le postulat de Maxwell n’est plus soutenable.




This new approach of the polarization of light has a main theoretical consequence. It questions the Maxwell's postulate. Certainly it was a great idea to merge light with the so called electromagnetic waves. Conversely this assumption that both are made of the propagation of turning electromagnetic fields appears today to be fully arbitrary and redundant. It shall be recognized that, at that time, there were not many solutions. The structure of atoms, as they are still considered, had been discovered only more than half a century later.


This hypothesis is arbitrary because it gives an electromagnetic nature to those waves, within themselves, on this unique fact that electromagnetic fields seem to play a part for their production within the frequency range low enough against light. Nevertheless this assumption is only arbitrary and probably physically meaningless, but not absurd. The redundancy is a more severe problem. It appears only with the discovery of the structure of atoms. Wave may induce, only by a mechanical behaviour, the displacement of electrons and an electromagnetic field is created by this displacement; otherwise there are two electromagnetic fields in the meantime one from the wave the other one from the electrons’ displacement. It is of no use to assume that the waves are electromagnetic fields by themselves.


The result of arbitrary, the result of redundancy, the result independence of waves from any electromagnetic field and from any kind of charge is that the Maxwell's postulate is of no use.



On peut envisager une preuve supplémentaire, non pas de la nature même de la polarisation de la lumière, car aucune expérience ne pourra jamais prouver une théorie, seule l’erreur se prouve, mais de l’indépendance de la polarisation à l’égard des champs électromagnétiques. Ce fut d’ailleurs l’objectif initial de la construction du tube à diaphragmes. Au lieu d’observer la couche K, il était prévu d’examiner la lumière réfléchie par un faisceau d’électrons dans le plan de la Galaxie. A défaut de connaissance des ordres de grandeur, il était envisagé d’utiliser le faisceau d’un tube de Perrin, acquis à cet effet, et des sources lasers. L’observation de la lumière réfléchie était prévue à l’aide d’une monture spéciale permettant une rotation de 360° dans un plan vertical contenant le centre de la Galaxie et de viser le centre de la Galaxie. Une première série de mesure a été réalisée en vision directe avec des LEDs fixées à l’obturateur du tube à diaphgrames. Aucune polarisation de la lumière émise par les LEDs n’a pu être observée. L’idée d’utiliser la lumière réfléchie par les électrons de la couche K dans le plan de la Galaxie est venue avant même de commencer le montage du tube de Perrin.


L’observation de la couche K a permis de calculer le flux lumineux nécessaire pour observer la polarisation dans le cas du tube de Perrin, puisqu’elle donne un ordre de grandeur mesurable. Le résultat est qu’il faudrait un faisceau d’électrons dix fois plus étendu et cent fois plus dense que celui du tube de Perrin, observé longitudinalement dans un tube sous vide de dix mètres de long et avec un faisceau lumineux de mêmes dimensions transversales que le faisceau d’électrons de 100 kW. Tout cela n’est pas irréalisable, mais inaccessible financièrement.




The full independence of the light polarization from the electromagnetic fields could be shown by another experience, although this would not be a proof of the nature of light, as proposed by this report. No experience can prove a theory ; only errors can be proved. The diaphragm tube was assembled in fact for this experience, and adapted later on for the observation of the K layer of the Sun. It was intended for measuring the polarization of light reflected by the electron beam of a Perrin's tube, bought for that purpose, in the direction of the Galaxy center. It was easier to train the tube toward the galaxy center than toward a point of the Galaxy plane. A special mount had been erected for that purpose. A first series of measurements had been performed with LEDs directly observed through the diaphragms. No polarization was found. The idea to measure the polarization of the K layer of the Sun in the  Galaxy plane came to mind before the Perrin's tube was attached to the diaphragm tube.


The observation of the K layer allows for calculating the lighting needed to be able to observe the polarization with an electron beam as it gives an order of magnitude of a measurable phenomenon. The result is that the electron beam shall be ten times as large as the one of the Perrin's tube, while it shall be hundred times as dense and as long as ten meters. The lighting power shall be about 100 kW. All that is not technically fully impossible but out an individual budget.

Il devient maintenant impossible de rester sur une position purement abstraite. Bien plus les raisonnements enchaînés dans l’introduction n’ont qu’une apparence de rigueur. On s’est efforcé de rester sur un plan purement conceptuel, mais sans support physique de la gravitation et de la lumière la tentative est un exercice de haute voltige, comme le sont tous les nominalismes et l’axiomatique en particulier. Avant de passer au modèle physique sous-tendu par les développements conceptuels, une remarque s’impose.


Pour des raisons psychologiques, semble-t-il, notre époque trouve dans Léonard de Vinci un modèle, non seulement de l’Art, mais aussi de la pensée. Or son idée que la connaissance procède d’abord de l’expérience est une absurdité insondable. Avec un tel principe, nous en serions toujours à l’âge de pierre. On ne trouvera jamais des tubes de Torricelli en haut du Puy de Sancy. Il fallait l’y monter, ce qui implique l’objectif, la pensée d’abord. Dans le même ordre d’idée, on a observé la décomposition de la lumière par les prismes pendant des siècles, avant que Newton, par une série de mesures parfaitement structurée, sans autre dispositif qu’un tel prisme, ne découvre la nature ondulatoire de la lumière. Or c’est l’objectif, la pensée, qui a structuré l’expérimentation. La pensée précède l’expérience, toujours. L’observation au hasard permet des découvertes, ainsi des galaxies et du décalage vers le rouge par Hubble, mais il n’est jamais arrivé que l’explication sorte du hasard.


Les faits s’imposent, évidemment. A les nier ou à les contourner, on voile seulement l’erreur. Mais la science n’est nullement une accumulation de faits. C’est d’abord une démarche cohérente enchaînant les faits et les provoquant surtout.



It is now necessary to leave a purely abstract position to present some other consequences. The reasoning presented within the introduction of this report have only the appearance of logic. Remaining on a purely nominalist level, without any physical support for light and gravitation, is purely a style exercise. There is no limit on what shall be considered as unrealistic for the axiomatic development presently considered as the only way for knowledge. In the mean time another way is also wide-spread.


For psychological reasons, Leonard da Vinci is taken as a model for both Art and thinking. But this idea that knowledge proceeds first from experience is so far the most unfathomable nonsense. With such a principle, the human being would have remain at the age of stone. The decomposition of light by prisms was known many centuries before Newton, using only such a simple prism, discovered the undulating nature of light after a fully structured series of measurements. The series were structure only by his mind toward his objective. Within the same range of situations,Torricelli's tubes will never be found at the top of the Puy of Sancy where Pascal's brother in law measured the atmospheric pressure decrease with altitude. He first brought it there. And Pascal asked him to do so because he has first an idea, an objective. Thinking comes always first, before experience. Some discoveries are the results of observations made by chance, such as the discovery of galaxies and redshift by Hubble. But the explanation never occurs by chance. Facts shall of course be taken into account, otherwise there is only place for errors. Nevertheless, Science is not an accumulation of facts. Science is first a consistent succession of facts linked to one another and mainly emerging from an objective.




Mais, bien sûr, c’est une démarche sans issue, pour deux raisons : elle est conditionnée par le contexte dans lequel nous vivons. A celui des mathématiques, dans un cadre mécaniste, qui a prévalu sans partage pendant plus d’un siècle, succède celui des modèles physiques dont le plus marquant est certainement la plasto-élasticité dans l’étude du mécanisme de la rupture des matériaux. L’autre raison est qu’elle n’a pas de fin. La cause première ne serait que la phrase qui l’énonce. C’est dire aussi que l’on ne peut échapper au nominalisme. Il faut bien commencer par des hypothèses à défaut de connaître la totalité de la Nature de l’infiniment grand à l’infiniment petit.


32 La gravitation et la lumière


Puisque la polarisation est considérée comme la propagation, si l’on peut dire, d’une lacune de moment cinétique, qui peut être provoquée par une lacune de moment cinétique liée au système de la gravitation, l’induction est que la lumière et la gravitation utilise le même support. C’était l’essentiel du système de Descartes. Le reste, qui a surtout été retenu, tient dans ses tourbillons. C’est un autre problème; il convient toutefois de noter au passage que Descartes a consacré la moitié de sa Théorie du Monde à expliquer comment ses tourbillons équilibrent la force centrifuge. Aussi est-il très difficile de comprendre pourquoi Newton a condamné la théorie de Descartes sur ce seul argument qu’il n’aurait pas équilibré l’accélération centrifuge.


Ironie de l’histoire de sciences, les tourbillons de Descartes ont une application industrielle : les gyrocyclones. En réalité, Newton avait doublement tort car le phénomène prévu par Descartes est encore plus fort qu’il ne le pensait puisque les impuretés solides se rassemblent dans l’axe et à la base des gyrocyclones.



But, of course, the step has no end, and for at least two reasons. First, it is depending upon the world we live in. After the kingdom of mathematics, where now something appears to be rotten, it is the time for physical models. The most conspicuous of those models is certainly the plasto-elasticity used for the study of the material breaking. No doubt, other times will come. The other reason is that nobody knows the very nature of things. That is to say that there is no chance to escape to the nominalism. Hypothesis cannot be avoided.


32 Gravitation and light

As polarization of light is considered as the propagation of a lack of angular momentum which may result from a lack of angular momentum within the gravitation system, it is assumed that light and gravitation have the same support. It is the main aspect of the Descartes' system. The other aspects are related to his whirls, and they have only been kept in mind. As far as these whirls are concerned it shall be noticed that half the World theory was devoted by Descartes to the balance of the centrifugal force. Thus it is very difficult to understand why Newton has condemned the Descartes' theory on this single fact that he would have not balance the centrifugal acceleration.


By an irony of Science history, the Descartes' whirls have an industrial use in the so-called gyrocyclones. In fact, Newton was wrong. Even more, the phenomenon used by Descartes is twice what he thought because the solid wastes are gathered in the axis at the bottom of the gyrocyclone.


Continuer ici à accumuler les hypothèses, rendrait la démarche douteuse. En fait cela résulte de l’ordre dans lequel on a voulu présenter les choses. Des principes et des faits, on a déduit un certain nombre d’hypothèses enchaînées les unes aux autres. Mais on peut procéder d’une manière plus simple: poser une hypothèse et lui appliquer les principes en accord avec les faits. Cette démarche fut bien évidemment la première. On s’est seulement efforcé de retarder autant que possible l’instant où, à l’évidence, les yeux vont se fermer et les oreilles se boucher, si tant est que cela ne ce soit pas déjà produit à la seule évocation d’un support pour la lumière et la gravitation. L’Ether revient: c’est l’horreur!


Que ce nouvel Ether n’ait rien de commun avec celui de Lorentz, qu’importe, l’Ether c’est l’horreur, exclue a priori.


Qu’importe si personne ne veut l’admettre. L’Ether remplissait l’Espace, comme l’air l’Atmosphère, bien avant que l’homme n’existe, et le remplira encore bien longtemps après sa disparition. Bien plus, sans Ether la matière n’existerait pas.


Qu’est-ce que l’Ether à présent? Un fluide composé de corpuscules. Ces corpuscules se trouvent en état d’agitation brownienne, avec naturellement une vitesse moyenne quadratique d’agitation exactement égale à la célérité de la propagation des ondes dans cet Ether, mais ils ont aussi un moment cinétique réparti statistiquement également, ce qui n’est pas le cas dans les fluides composés de molécules aux formes plus ou moins complexes et dont la rotation propre se trouverait d’ailleurs gêné par l’Ether.




It could be though that adding there a new hypothesis would jeopardize the attempt to propose a new approach. But this is only the result of the way this approach has been presented up to now. Starting from principles, several consequences, appearing as hypothesis, have been deducted from one another. Nevertheless, there is another way to present the new approach. That is to begin with one single hypothesis and to proceed by deductions applying the principles in compliance with experiments. This method was of course used first. The reasoning here above was intended to delay this very moment where eyes will close and ears will stop, if indeed that has not already occurred when it has been envisaged that light and gravitation need a support. Ether is coming back! What a shame!


Although this new Ether is not a solid but a fluid and as such has no connection with the Lorentz’s Ether, it does not matter. Ether is a shame; fully unacceptable! Those who are so proud of the past changes, do not want now to change anything. Whatever they say Ether fills space, like air fills the Atmosphere. In addition, matter cannot exist outside Ether.


Ether is now a fluid made of corpuscles. Within this fluid, the propagation speed of waves is exactly the quadratic mean brownian speed. In addition the corpuscles have their own angular momentum, also statistically distributed. This is not the case of air, water or similar fluids, where the molecules have intricate shapes so that spinning is not possible. Moreover spinning would be impeded by Ether.



Toutefois, dans la propagation des ondes dans l’Ether, ondes nécessairement longitudinales, seule la composante transversale du moment cinétique peut se transmettre.


Ces ondes sont créées par le mouvement des corps dans l’Ether. Mais c’est principalement les mouvements des électrons qui sont à l’origine de la plupart des ondes de l’Ether utilisables pratiquement comme les ultraviolets, l’infrarouge ou les ondes dites électromagnétiques. Les électrons peuvent ainsi provoquer dans l’Ether des petits trains d’onde de même dimension transversale que la leur. Chacun de ces petits trains d’onde transmet la composante transversale du moment cinétique qui lui a été communiquée par son électron générateur. Chacun de ces petits trains d’onde constitue ce qui a été appelé un photon, mais, dans l’éther, le photon n’est pas un corpuscule, mais un train d’onde propageant une énergie ondulatoire bien définie et fonction du mouvement de son électron générateur. La quantification des sauts d’électrons suffit pour quantifier les énergies de ces trains d’ondes. C’est par là une autre redondance des théories actuelles qui disparaît. Il n’est pas nécessaire de quantifier les photons, qui peuvent naturellement transmettre le spectre continu de tous les niveaux d’énergie. Mais justement, tous les niveaux ne sont pas possibles puisque les sources, ces sauts d’électrons, sont quantifiées. En particulier, plus rien ne s’oppose à la variation de l’énergie transmise, problème sans doute le plus irritant de la quantification des photons eux-mêmes, quantification qui devient, il faut le répéter, parfaitement inutile.




However, during the longitudinal wave propagation in Ether, only the transverse angular momentum can be transmitted.


These waves are generated by the motion of bodies in Ether. Mainly they are generated by electrons’ motions. UV, infrared, and the so called electromagnetic waves, are a result of these electrons’ motions. Each electron generates a small wave string with the very same length wave as the electrons' motion itself, with the same transverse dimension and with the same transverse angular momentum. Each of those small wave strings has been called a photon, but now the photon is no more a particle. It is a wave string propagating longitudinally an undulating energy directly dependent upon the frequency of its generating electron. Quantification of the electron’s jumps is sufficient for quantifying the wave string energy. This was another redundancy of the former approach. It is absolutely useless to quantify the photons as long as their sources, the electron jumps, are already quantified. Thus photons may transmit the continuum spectra. But all levels are not allowed because electrons’ jumps are quantified. Moreover the energy transmitted by photons may change during the propagation; this was a major inconsistency of the former approach including a quantification of the photons themselves.




Au passage, on aura bien sûr éliminé l’objection possible sur la dispersion de ces petits trains d’ondes. Il suffit pour cela de considérer que les corpuscules qui composent l’Ether sont suffisamment sphériques pour propager leur ébranlement seulement longitudinalement. D’un autre côté, ils ne peuvent être parfaitement lisses, autrement, il serait difficile de concevoir comment il pourrait transmettre un moment cinétique.


Contrairement à ce que pensait Descartes, les tourbillons ne peuvent être que la conséquence d’un autre phénomène et non la raison de la rotation des astres. Pour expliquer la gravitation par ce nouvel Ether, il faut tenir compte d’un fait qui n’a rien changé aux théories actuelles malgré son énormité. Le fait que la matière soit pratiquement vide n’est vraiment admis sans réserve que depuis soixante ans, c’est à dire très largement après l’élaboration des grands postulats de l’optique et de la gravitation. L’Ether remplit tout l’Espace, y compris entre les atomes et l’intérieur même des noyaux des atomes qui doivent, de toute nécessité, être des bulles, seule structure dont la masse, à épaisseur donnée,soit proportionnelle à la surface apparente, là aussi condition essentielle pour qu’un fluide ait une action proportionnelle à la masse.


Il faut que l’Ether se condense dans la matière pour que les corps soient comme attirés les uns par les autres. Au passage, on aura noté aussi qu’ainsi l’Ether constitue la matière où il se condense, du moins dans les lieux de l’Espace où nous observons une condensation, car rien n’exclut qu’il y ait des lieux où, au contraire, la matière s’évapore en Ether.





Many objections may come to mind. The first, certainly, is the dispersion of such wave strings. There is an easy answer. The corpuscles of Ether shall be as similar to spheres as possible, so that only the longitudinal motion is transmitted. On another hand, they cannot be perfectly smooth otherwise they would not be able to transmit an angular momentum.


Descartes’ whirls cannot exist and continue by themselves. They are a consequence of another phenomenon and not the root cause of the rotation of all heavenly bodies. It is necessary to take into account one of the most drastic change in the knowledge we have about matter : it is nearly fully empty. This is now fully accepted for sixty years, that is to say a long time after all the postulates related to light and gravitation were proposed.


Ether fills Space from its most remote parts down to the inside of atoms and even down to the inside of the atoms’ kernel. Atoms’ kernel shall be bubbles so that the effect of an Ether stream on them can be proportional to their surface. This is an essential condition achieving the proportionality of Ether streams action to the mass of atoms.


Then Ether shall condense inside the atoms’ kernel so that bodies may be attracted by one another. This is an appearance of course; they are not attracted, but pushed reciprocally by the condensation stream of other bodies. Thus matter in made of Ether. Such a condensation may not be general; there may be places in Space where matter vaporizes in Ether.




Et c’est là que reviennent les tourbillons de Descartes. Pour les corps assez massifs, la condensation provoque une mise en rotation. Le phénomène est en réalité très complexe et on est conduit à constater l’existence, d’ailleurs justifiée par les principes, d’une double série de tourbillons alternés autour de ces corps que sont les astres.


La rotation de l’Ether dans les tourbillons conduit à expliciter le concept de défaut potentiel de moment cinétique utilisé dans l’introduction. Le moment cinétique des corpuscules de l’Ether en rotation dans les systèmes galactiques ou planétaires, doit être compensé. Cette compensation se fait au détriment du moment cinétique propre de ces corpuscules. Le concept utilisé pour une présentation aussi acceptable que possible des choses, devient une réalité. Il y a un défaut effectif dans la répartition statistique des moments cinétiques des corpuscules de l’Ether. Les degrés de liberté des corpuscules se trouvent limités et ainsi les équations du mouvement modifiées. D’une variation de la vitesse tangentielle en 1/d, on passe à une variation en 1/d par une zone à vitesse constante.


L’objectif ici n’est pas de développer entièrement ce nouveau modèle de la gravitation dans son ensemble, mais d’en donner les éléments essentiels suffisants pour compléter le tableau relatif à la lumière. On vient de répondre à tous les points soulevés relatifs à la polarisation de la lumière, mais il y a bien d’autres conséquences pour la lumière. Et d’abord la déviation de la lumière par les astres, phénomène prévu par Descartes, mais le calcul montre que les tourbillons de Descartes ne donnent que la moitié de la valeur mesurée, l’autre moitié résulte de la condensation que l’on pourrait appeler l’effet Newton.




There whirls may come back. For heavenly bodies large enough, the condensation generates a rotation. The phenomenon is quite complex and in fact, the equatorial whirl is surrounded by two alternate series of whirls on each side. This is for complying with the Hamilton principle.


Rotation of Ether within those whirls allows for explaining physically the angular momentum lack as defined in the Introduction. The angular momentum of the Ether’s corpuscles, shall be compensated. The compensation is done by pumping in the proper angular momentum of these corpuscles. The concept use for the presentation of the polarization of the K layer is now physically existing. This is an effective lack in the statistical distribution of the Ether particles’ angular momentum. The freedom degrees of these corpuscles are thus limited and the equations of the motion of Ether streams are modified accordingly. From a tangential speed variation as 1/d, it becomes as 1/d, after a constant tangential speed intermediate zone.


This is not the objective of this report to develop a full model for gravitation, but only to give the main issues necessary to understand the main properties of light.


Beyond the polarization of light; there are other consequences for light. First it shall be deflected by heavenly bodies like the Sun. This had been foreseen explicitly by Descartes, but his whirls only account for half the measured deflection. The other half is a result of condensation and could be designated as Newton’s effect.




Puisque ainsi c’est l’Ether qui entraîne la Terre en rotation autour du Soleil, bien évidemment il serait absurde de chercher à mettre en évidence un mouvement de la Terre par rapport à l’Ether. C’est pourtant ce que Morley et Michelson ont essayé avec leur fameux interféromètre, sans succès évidemment, mais il pensait à l’Ether absolument immobile de Lorentz, un autre monde!


Par contre, si vous faites tourner la lumière dans deux sens différents grâce à des miroirs disposés à la périphérie d’un disque, à la surface de la Terre, où l’Ether est pratiquement au repos, bien sûr vous devez observer un décalage dès que le disque se met à tourner. C’est ce que Harress et Sagnac ont tenté et ils ont réussi. Comble de l’ironie de l’histoire des sciences, l’interféromètre de Michelson n’a aucune application pratique dans le domaine pour lequel il a été conçu, alors que le disque de Sagnac équipe tous les avions récents et les bas étages des fusées sous le nom de gyrolaser.


L’interféromètre de Michelson a entraîné un immense bouleversement des théories alors que l’appareil de Sagnac, largement postérieur n’a rien changé en retour. Comble de malheur, son résultat reste totalement inexpliqué. Il y a eu de nombreuses tentatives, toutes sont dédiées, la plupart comportent des hypothèses spécieuses sur le mode de réflexion. Une seule est générale et admise par toute la communauté scientifique.


A défaut de métrique non euclidienne représentant la répartition des accélérations dans la rotation d’un solide, on a cherché à démontrer que la Relativité Restreinte pouvait donner une première approximation du résultat obtenu par Sagnac. Le calcul conduit d’ailleurs à une excellente approximation, mais il comporte une erreur fatale.




As the Earth is dragged by Ether it would be a nonsense to try to found any motion of the Earth with respect to Ether. Nevertheless that had been tried by Morley and Michelson with their famous interferometer. They failed of course, but they had in mind that motionless absolute Lorentz’ Ether, another world!


Conversely, when light is turning around a disk fitted with mirrors for that purpose, in the two opposite ways, of course a shift of the central fringe shall occur as soon as the disk is set turning. The disk is turning with respect to ether while Ether has no motion with respect to the Earth. That had been tried by Harress and by Sagnac. They succeeded of course. The most surprising is that the Michelson’s interferometer has no use within the frame of its purpose although the Sagnac disk is used within all recent planes and within lower parts of space rocket. It is known as the gyrolaser.


the Michelson’s interferometer negative result introduced a wide change within the theoretical world, while the Sagnac positive result, coming too late, did not change anything. But the worst of all is that the Sagnac’s result remains desperately unexplained. All tentative explanations are dedicated and introduce generally a specific hypothesis on the reflection not use elsewhere. It was not possible to found a book in English where the only known solution is explained. Even worst, Sagnac and Haress seem to be unknown. For this reason, reference is made here after to the French publication "Les vérifications expérimentales de la Relativité Générale" (Masson et Cie, 1964).




On se réfère ici à la présentation facilement accessible donnée dans l'ouvrage "Les vérifications expérimentales de la Relativité Générale" (Masson et Cie, 1964). On passera sur le fait que le passage d'un domaine d’intégration au domaine tangent, à un instant donné, est un exercice de la plus grande audace, eu égard au fondement même de la Relativité. L'auteur soi-même s'en excuse, en quelque sorte, quelques pages plus loin, reconnaissant le caractère, au fond absurde, de la démarche, et affirmant l'impérieuse nécessité d'avoir recours à une solution non-euclidienne qui, par malheur, reste encore à trouver. Ne nous étonnons pas davantage, que l'auteur intègre une différentielle de temps de parcours le long du contour du disque et non le long du parcours de la lumière, ce qui confirme la confusion volontaire mentionnée d'abord.


Considérons seulement l'impressionnant développement qui s'étale de la page 68 à la page 81, et allons d'emblée au résultat V-56. La différence de temps de parcours entre les rayons lumineux parcourant la périphérie du disque en rotation, mais chacun dans un sens, est de 4wSi(0) /c2, c'est-à-dire proportionnel au double de l'angle d'intégration q=2p comme on peut d'ailleurs s'en assurer par V-52. En conséquence la différentielle de la différence de temps de parcours doit être proportionnelle à la différentielle de q. Comment la différence des écarts pourrait-elle différer de l'intégrale de la différence des différentielles? Or cette dernière intégrale reste désespérement identiquement nulle comme on peut s'en assurer en regardant seulement l'équation V-50. En application des principes relativistes, le signe du second terme de la parenthèse ne peut changer en aucune circonstance. Le gyrolaser reste inexpliqué.


Il réserve en outre une surprise de taille. Placé dans un satellite géostationnaire, il ne doit pas indiquer de rotation dans le plan équatorial de la Terre, par analogie avec l'interféromètre de Michelson dans le nouvel Ether.


As a non Euclidean metric has never been found to accommodate the acceleration distribution for a spinning body, the author proposes to find an approximation using the Relativity, although she recognizes that only a non Euclidean solution is allowed. Nevertheless, the result is perfect, unfortunately there is a fatal error in the calculations.


Notwithstanding that it is not allowed by the Relativity postulates to switch from one space to the tangent one at a given time, the author performs the integration of the light course time differential along the disk circumference and not along the path of light. But this is only to confirm that the relativity postulates are not implemented as already said.


The result is that the difference between both light paths along the rotating disk is
wSi(0) /c2, that is to say proportional to twice the integration angle : q=2p. As a consequence , the differential of the difference between the light path duration is proportional to q. Now then, the difference between the time gaps is equal to the integration of the difference between the differentials. The problem is that this difference remains unfortunately permanently as low as zero as it is stipulated by the relativist postulates. The gyrolaser remains unexplained.


Furthermore there is an additional problem. When fitted within a geo-stationary satellite, the gyrolaser shall not show any rotation in the Earth equatorial plane. The reasoning is similar to the Michelson’s result within the new Ether.








Les conséquences de la seconde variante

de la troisième

hypothèse du Professeur Allais

pour expliquer les résultats de

ses analyses des mesures

interférométriques de Miller




The consequences of Pr. Allais'

second option of his third hypothesis

to explain

the results of his analysis

of Miller's

interferometer measurements.








0ctober 1997, March 1998



This report is public. Its use as a whole or the use of any part thereof cannot involve any subsequent right.

Ce rapport n'est couvert d'aucune protection. Son utilisation, en tout ou partie, ne peut générer aucun droit.









Sommaire/ Summary :








       E vidi gente , por lo vallon tondo ,

 Venir tacendo , e lagrimando , al passo ,

Che fanno le letàne in questo mondo.



       Come 'l viso mi scese in lor piu basso,

Mirabilmente apparve esser travolto

Ciascun dal mento al principio del casso :



       Che nalle reni era tornato 'l volto ,

E indietro venir li convenia ,

Perchè 'l veder dinanzi era lor tolto.





Les résultats obtenus à l'interféromètre de Michelson par Miller ont été analysés par le Professeur Allais. Il en résulte une incontestable corrélation entre la vitesse mesurée et la position spatiale de la Terre au cours de l'année.



Ce résultat est tout à la fois contraire à la théorie de la relativité et à la théorie de l'éther de Lorentz.


Le Professeur Allais a proposé trois interprétations.


La première associe d'une anisotropie de l'espace avec l'interprétation de Michelson et présente, comme la relativité, l'inconvénient de ne pas apporter de réponse à l'expérience de Sagnac. Elle n'a donc pas été examinée davantage.


La seconde interprétation associe l'anisotropie de l'espace avec une anisotropie résultant des vitesses cosmique et orbitale de la Terre. Cette interprétation n’apporte pas davantage de réponse à l'expérience de Sagnac. De plus, il n'a pas été possible de comprendre comment les anisotropies peuvent compenser en permanence le complément des vitesses mesurées par Miller à la vitesse de la Terre, alors que sa direction est variable au cours de la journée et de l'année sidérale. Il faut bien expliquer que 75% de la vitesse de la Terre autour du Soleil reste indétectable en permanence.


La troisième interprétation reprend la nécessité de l'anisotropie astronomique et comporte en fait deux possibilités : soit la Terre entraîne l'éther, soit l'éther entraîne la Terre. Bien entendu, ces deux possibilités sont conformes à l'expérience de Michelson, mais également à l'expérience de Sagnac.


En l’absence de matière, l’éther ne peut être entraîné que par les champs de gravitation ou magnétiques, dans le cadre des connaissances actuelles. Il convient de noter que les astres se déplaceraient ainsi avec un nuage d’éther, plus étendu, dans le cas de la Terre, que l’atmosphère.


Dans un système planétaire, comme dans les galaxies d’ailleurs, l’éther serait entraîné par les astres dans leur mouvement autour de l’astre central.


Deux cas peuvent alors être envisagés. L’éther pourrait être entraîné également en rotation. Le Soleil entraînerait ainsi l’éther dans son mouvement orbital autour de la galaxie, mais cette couche autour du Soleil serait elle-même entraînée en rotation autour du Soleil. Dans ces conditions, l’expérience de Michelson serait expliquée de manière redondante, puisque la Terre tourne avec l’éther entraîné en rotation par le Soleil et par elle-même dans son mouvement orbital.


Une conséquence nécessaire est l’impossibilité d’un éther solide exigé par la transmission d’ondes transversales comme le sont les ondes électromagnétiques. Mais ceci est commun à toutes les solutions basées sur un entraînement ou un mouvement de l’éther et la solution à ce problème constitue justement un aspect essentiel de toute approche de ce genre. Un autre problème majeur est évidemment la symétrie axiale des rotations de l’éther avec les astres. Enfin, cette solution pose le problème des frottements dans l’éther, mais c'est un problème commun à toutes les solutions comportant un éther. Cependant, la redondance des explications des résultats de Michelson est probablement fatale à cette variante.







Le cas où les astres n’entraînent pas l’éther en rotation, mais seulement en translation, permet d’éliminer la redondance de l’explication de l’expérience de Michelson, et la symétrie axiale. Cette solution est aussi acceptable a priori que la variante de l’entraînement des astres par l’éther. Elle n’a pas été retenue, car il apparaît incohérent de penser que l’entraînement ne peut exister qu’en translation et non en rotation. A tout le moins, il devrait exister une rotation sidérale, dans le cas de la Terre, de 360° par an.


Bien qu’aucun argument définitif ne permette de rejeter d’emblée ces variantes des interprétations des mesures de Miller analysées en temps sidéral, c’est la seconde variante de la troisième interprétation proposée par Professor Allais, qui a retenu par les ingénieurs associés dans leur théorie de l'Espace.


Il faut rejeter l’éther solide bien sûr, mais l’entraînement des astres par l’éther explique avec la même simplicité l’expérience de Michelson et celle de Sagnac, sans redondance.



La nature transversale de la lumière ne peut pas être expliquée par la mécanique des fluides. Les ingénieurs associés ont donc proposé une modification radicale en introduisant les fluides à six degrés de liberté. Le moment cinétique des corpuscules de l'éther permet de rendre compte des propriétés transversales de la lumière.

The results obtained with the Michelson interferometer by Miller were analysed by Pr. Allais. The result is an undeniable correlation between the measured speed and the spatial position of the Earth during the year.



This result is contrary both to the theory of relativity and theory of the ether of Lorentz.


Pr. Allais proposed three interpretations.


The first involves an anisotropy of space with the interpretation of Michelson and, like relativity, the disadvantage of not providing an answer to the experiment of Sagnac. It was therefore not considered further.



The second interpretation involves the anisotropy of space with an anisotropy resulting of the cosmic and orbital speed of the Earth. This interpretation does not answer to the experiment of Sagnac either. Moreover, it was not possible to understand how those anisotropies may balance permanently the part of the speeds measured by Miller coming in addition to the speed of the Earth, while its direction is variable during the day and the sidereal year . One must explain that 75% of the speed of Earth around the Sun remains permanently undetectable.


The third interpretation still involves the need for an astronomical anisotropy and an alternative between two additional possibilities. Either the Earth drags the ether or the ether drags the Earth. Of course, these two possibilities are consistent with the Michelson experiment, but also the experience of Sagnac.


In the absence of matter, ether could be dragged only by the gravitational or magnetic fields, in the context of current knowledge. It should be noted that the stars would move with a cloud of ether, greater than atmosphere in the case of the Earth.


In a planetary system, as in the galaxies, the ether would be dragged by the stars in their motion around the central star.


Two cases may then be considered. Ether could also be dragged in rotation. The Sun would drag the ether in its orbital motion around the galaxy, but this layer around the Sun would itself be dragged in rotation around the Sun. In these conditions, the experiment of Michelson would be explained redundantly, as the Earth rotates with ether dragged in rotation by the sun and by itself in its orbital motion.



A necessary consequence is the impossibility of a solid ether required by the transmission of transverse waves, as are the electromagnetic waves. But this is common to all solutions based on a drag or a motion of the ether and the solution to this problem is just an essential part of any approach of this kind. Another major problem is obviously the axial symmetry of the rotations of ether with the stars. Finally, this solution raises the problem of friction in the ether, but it is a problem common to all solutions involving an ether. However, the redundancy of the explanations of the results of Michelson is probably fatal to this variant.







The issue not involving a drag of the ether in rotation by the stars, but only in translation, may eliminate the redundancy of the explanation of the Michelson experiment, and the axial symmetry. This solution is as acceptable a priori as the alternative involving the drag of the stars by the ether. It was not accepted because it is inconsistent to suggest that dragging can exist in translation only and not in rotation. At the very least, there should be a sidereal rotation, in the case of the Earth, 360° per year.


Although no definitive argument allows for rejecting these alternative interpretations of Miller measurements analysed according to the sidereal time, the second variant of the third interpretation proposed by Mr. Allais, has been chosen by the associates engineers for their theory of Space.


One must reject the solid ether of course, but the dragging of stars by ether explains with the same simplicity both experiments of Michelson and Sagnac without redundancy.


The transversal nature of light can not be explained by fluid mechanics. This is why the associated engineers proposed a drastic change by introducing the notion of fluid with six degrees of freedom. The angular moment of this ether fluid corpuscle answers the transversal issue.









The inversion of the electron magnetic property

and its implication.











May 2014


This report is public. Its use as a whole or the use of any part thereof cannot involve any subsequent right.

Ce rapport n'est couvert d'aucune protection. Son utilisation, en tout ou partie, ne peut générer aucun droit.


I wish to thank all scientists who help me making this paper as clear as possible.



Abstract : This paper is related to the definition of electron. A first inversion was done when attributing to the electrical currents the wrong direction. But a second inversion could have been done for the magnetic property of the electron. An experiment is proposed to confirm this inversion.


Résumé : Ce rapport concerne la définition de l’électron. Une première inversion a été faite en attribuant aux courants électriques le mauvais sens d’écoulement. Mais une seconde inversion aurait pu se produire pour les propriétés magnétiques de l’électron. Une expérience est proposée pour confirmer cette inversion.



Key words: Electron ; magnetic field ; magnetic moment ; cathode ray ; electrical current ; electric field.


1. Electron definition inversion

2. The proposed experiment

3. Figures

4. References








1.  Electron definition inversion


The electric current within conductors was first given the wrong direction before discovering electrons. The same inversion could have been done when defining the intrinsic magnetic property of electrons. The wrong solution would have been choosen in both cases.


1.1       The standard model of the electron.

The electron is a lepton with a negative elementary electric charge. The invariant mass of an electron is approximately 9.109×10−31 kg.; their electric charge is −1.602×10−19 coulomb. They have an intrinsic angular moment or spin of 1⁄2. In additions electrons has an intrinsic magnetic moment along its spin axis. It is approximately equal to one Bohr magneton, which is a physical constant equal to 9.27400915(23)×10−24 joules per tesla. The orientation of their spin with respect to their magnetic moment defines the helicity. Electrons have zero colour charge. Electrons have properties of both particles and waves.


The electron is considered within the standard model as a magnetic dipole, characterized by its intrinsic magnetic moment. So that it is analogous to a tiny bar magnet.


In line with the axiomatic approach, it is postulated by Quantum Mechanics that the magnetic moment of electrons is always kept stochastic both within conductors and within cathode rays which are said to be unpolarized. As the magnetic moments of electrons are distributed at random, they would not create any magnetic field.


If the existence and properties of electrons have been subjected to many experiments, it appears that the Rowland’s disk is the only experiment used to demonstrate that the motion of electrons is the cause of magnetic field of conductors.


The problem of obtaining a magnetic field by moving charges along a straight line is linked to the MHD (magneto hydrodynamics), the dream of the 1960 to produce directly electricity without turbine. It fails. There are only few experiments which succeeded to obtain a very small effect but they used superconductors where, I am convinced, the main part is played by the atomic structure and not by the single fact of moving the charges.


1.2              The Maxwell equations (in void)


Where J is the product of the charge density by the mean speed of charges:


The second term of the fourth equation  has been added by Maxwell to the Ampere equation. It was formerly call the displacement current. When there is no current  is null. This is the Maxwell-Hertz equation. The main solution of this equation is a wave function which Maxwell assume to be the equation of light. The problem is that when there is no current  then there is no moving charges, there is no field variation either, so that the term  should also be null. So that, the Maxwell-Hertz is presently no more considered as a consequence of the Maxwell-Ampere equation, but as a postulate.


Nevertheless this term was maintained because it explains that capacitors being charged have a magnetic field.



1.3              The inversion of the intrinsic magnetic moment definition.


An inversion could have occured in the definition of the intrinsic magnetic property of electrons of the standard model of Quantum Mechanics. Unlike the standard model of the electron in Quantum Mechanics, the intrinsic magnetic property of the electrons, call the magnetic moment, could not be similar to that of a small magnet.


The other solution is that electrons could have a magnetic field with the structure of an electric current.


The wrong definition was choosen as a result of a long history. The magnetic field of electrical currents is presently considered as an effect of the translation speed of electrons within conductors. This effect was first discovered by Gian Domenico Romagnosi in May 1802 and reported to the French Academy of Science which didn’t register the discovery. The Danish scientist Hans Christian Ørsted made the same discovery twenty years later and the Danish Academy published immediately his report. Nevertheless, Ørsted recognized that he was informed of Romagnosi’s experiment. The cathode rays were dicovered at the end of the 19e century. In 1895, the Perrin experiment shown they are negatively charged. Thomson made in 1897 the bold suggestion that cathode rays were material constituents of atoms and it turned out to be complying with all further experiments. At that time the Maxwell-Ampere law was modified to take into account the existence of electrons. But the cause of the magnetic field was not questionned. The electrical current was understood as a flow rate of electrons the other way round, opposite to the conventional direction of the electrical current.


The choice of the definition of the standard model of the electrons was considered to be confirmed by the Rowland’s experiment performed in 1876.


Nevertheless, in the Rowland’s experiment the disk rotates. This experience shows that the rotation of an electric charge produces a magnetic field, but a rotation cannot be considered as a translation. It is fully inconsistent to reject the explanation of the rotating disk of the Sagnac experiment as an effect of a translation and, in the mean time, to accept that the rotation of a charge could be equivalent to a translation. This link between charge rotation and magnetic field seems to be in fact in line with the standard model of electron.


There is another possible explanation, but it is less satisfactory. This experiment is very similar to Barnett’s experiment with a magnet. It could be deduced that magnets and conductors do have similar Weiss structures inside, but in the case of conductors, they are not correctly oriented so that normally there is no magnetic field. The rotation of the disk modifies the arrangement of electrons within the conductor by the Coriolis acceleration resulting from the centrifugal acceleration of the disk.


The consequence of this change in the electron magnetic property is that the magnetic field created by the intrinsic magnetic property of the electrons has the structure of the magnetic field of the currents as well as of cathode ray.


Consequently, the magnetic field of magnets can not result directly from the intrinsic magnetic moment of the electrons as in the standard model.


The magnetic field of the magnets results from the arrangement of electrons in circular structures, such as rings or coils, which would create therefore a field topology consistent with reality. The Weiss domains would be therefore structures different from that implied by the standard theory.


This inversion of field topologies would allow to consider a quantitative explanation of the Barnett’s effect which remains purely qualitative for the time being. One might think that the electron ring arrangements that causes the field of magnets are tilted by the Coriolis’ acceleration resulting from the centrifugal acceleration, giving thus an important amplification factor not included in the standard model of Quantum Mechanics.


The inversion of the magnetic field definition of electrons would have a consequence on the cause of the magnetic field of electrical current and cathode ray. There are presently two co-existing potential causes of the magnetic field by an electron flows: translation speed and “intrinsic magnetic moment”. The “intrinsic magnetic moment” of electrons is presently considered as a result of electron spinning, so that motion of the charge is considered as the only cause of magnetism. Nevertheless, within a conductor or within a cathode ray, electrons have finally two potential ways of producing the magnetic field. This is against the specific causal uniqueness principle applicable for basic concepts of physics as well as for geometry. It is also against the Ockham's simplicity principle. The inversion of the magnetic field definition of the electrons would make possible to attribute the magnetic field of electrical current and cathode ray directly to the electron magnetic property.



1.4              The modified Maxwell equations

The change is only related to the Maxwell-Ampere equation, this is the only term involved in the change of the electron magnetic definition inversion :




Where vector  is the Bohr’s magnetron as defined by the standard model of Quantum Mechanics, i.e. with the magnetic property of a small magnet, and  the density of electrons taking into account their average orientation. The induction  may have several components if there are several average orientations determined statistically from the electrons distribution. It may be added that the same apply to all particles owning what is call by the standard model an “intrinsic magnetic moment”.


The term added by Maxwell disappears because the magnetic field is always produced by the magnetic property of electrons. In the case of capacitors being charged, the magnetic property of electrons is oriented in the capacitor plate when they move within the structure of the conductive plate modified by the electric field and they are included in this new equation exactly as all other electrons in conductors and cathode rays correctly oriented. This is exactly what occurs within the cathode of the cathode ray gun. But, as in the capacitor the electrons are not ejected outside toward the anode, they loose their magnetic property orientation under the effect of unoriented electrons of the plate.


The field created by a cathode ray should result directly from the intrinsic magnetic property of the electrons, now inversed . This is the point which could be verified experimentally.



2. The proposed experiment


Electric fields don’t change the magnetic property of electrons. If the cathode ray is deviated up to 90 ° by an electric field, the intrinsic magnetic property of electron remains as it was, so that the magnetic field of the cathode ray should no longer be measured by coils placed in a plane containing the beam, unlike what can be observed before deviation.


A similar result would be obtained by a deviation by a magnetic field.


2.1       The deviation of the cathode ray by an electric field.

2.1.1    In the standard model of Quantum Mechanics, the electric field has no influence of the intrinsic magnetic moment of electrons as shown by Maxwell’s equations.


So that after the bend of the cathode tube nothing is changed within this theory and the second sensor shall measure the same magnetic field as the first sensor.


2.1.2    But if the definition of the intrinsic magnetic property of electron is inverted, and accordingly if the magnetic field of the ray is produced exclusively by the magnetic property of electrons instead of their motion, then there will not be any magnetic field measured by the second sensor, because this sensor is installed in a position enabling only to measure a magnetic field structure as generated by an electrical current. The magnetic field of the electrons is maintained as it was before the bend. It could be measured only by coils with their axis aligned with the ray axis after the bend.


2.2       The deviation of the cathode ray by a magnetic field.

2.2.1   A magnetic field will also deviate the ray by 90°. In the standard model, the electrons produce a magnetic field by their motion. They move with regard to the second sensor exactly as they move with regard to the first sensor before the bend. The magnetic field measured by the second sensor shall be exactly the same as by the first sensor.


There is a difference with the deviation by an electric field which nevertheless does not change the result of the measurement. In the standard model, the electrons are not polarized before the bend. But the magnetic field deviating the electrons should polarize the ray so that a complementary magnetic field should be measured after the bend. But it would not be measured by the second sensor because the overall intrinsic magnetic field of the electrons after deviation will have an induction colinear to the magnetic field used to deviate the electrons.


2.2.2    But here also, if the definition of the intrinsic magnetic property of electron is inverted, and accordingly if the magnetic field of the ray is produced exclusively by the magnetic property of electrons instead of their motion, then there will be also not any magnetic field measured by the second sensor, for the very same reason.


The magnetic field used for the 90° deviation of the ray will change the magnetic property of the electrons orientation, but the null result of the second sensor will not be changed. The electrons are assumed not to be like magnets but like currents, i.e. they have a magnetic field with an electric current magnetic field structure. So that a magnetic field induction will tend to align the electrons intrinsic magnetic field induction. As these inductions are in the opposite direction for diametrically opposed points around the electrons, thus the electrons will take an intermediary position. But this new state of their overall magnetic field cannot be measured by the coils as installed in the sketch, because the B vector are not in the right direction and furthermore it seems that they could cancel each other.


That does not reduce the interest of the deviation by an electric field, but the experience is much easier to achieve, because the magnetic field depends on the intensity, so that a low voltage may be used.


2.3. Experiment protocol   (see figure page 14)

The spherical portion of an original Perrin tube shall be replaced by a pyrex tube of 40 mm diameter bent at the middle by 90°. It could be for instance a NARVA PR2 tube still available in the Internet. Figures hereafter are suitable for this kind of tube.


The magnetic field of the cathode ray will be measured in the straight part of the modified Perrin tube and after the curved part. 


The anode voltage of 400 V to crest will be two waves rectified, but not filtered , so that the current induced in the sensor can be detected by an analogue to digital converter after an amplification by an Operational Amplifier with a factor of 200. The anode voltage will be maintained  throughout the  measurement. Cathod  heating will be supplied by a DC 6.5 V power supply.

The cathode ray deviation up to 90° will be obtained by an electric field produced by two semi-toroidal plates placed on each side of the tube in its curved part. They will be supplied with an adjustable DC power supply from 200 to 2000 V, rectified and filtered.


In this experiment, two identical sensors are needed with 12 coils of 1300 loops each connected to a resistor 1MW and connected to an operational amplifier with an amplification factor of 200.


One of the sensors will be placed before the curved portion of the tube and the other one after. Both signals delivered by the AD converter will be sent to a data acquisition module connected to a PC.


The first sensor should show the magnetic field of the cathode ray as it has been checked by the author in May 2000 with a straight tube. For a straight tube, the magnetic field of the cathode ray, measured by the author, had precisely the value calculated from the amperage of the cathode ray measured at the top of the tube in the same as in the Perrin’s experiment.


The second sensor, located after the 90° deviation of the cathode ray in the elbow of the tube, should show nothing in both cases of a deviation of the cathode ray by an electric field or by a magnetic field.


3. Figures

Example of a modified Narva PR2 Tube used by the author to measure the magnetic field of an electron ray magnetic field. The tube of the new experiment proposed by this paper shall be bent by 90° in the middle.







The coils and the overall experimental device for the straight tube. 


4.  References

Baigrie, B.               (2006).     Electricity and Magnetism: A Historical Perspective. Greenwood Press.

Bernard Pr. M.Y.    (1960)      Initiation à la mécanique quantique     Editions Hachette


Hennequin Pr. J.      (1970)      Electromagnétisme et relativité restreinte        Editions Dunod


Keithley, J.F.           (1999).     The Story of Electrical and Magnetic Measurements: From 500 B.C. to the 1940s            IEEE Press.

Landau Pr. L.          (1966)      Théorie des champs               Editions Mir, Moscou


Liboff Pr.R.L.          (1908)      Introductory Quantum Mechanics      Holden-Day Inc


Mach Pr. E.            (1908)      De la connaissance et de l'erreur        Editions Flammarion


Marinov S.              (1978)      Rotating disk experiments. Foundations of Physics 8 (1-2)


Pérez Pr.J.P.& alt    (1997)      Electromagnétisme     Editions Masson


Tonnelat Pr. M.A.   (1971)      Histoire du principe de relativité         Editions Flammarion
















Zonal effects




Physics Treaty



















Zonal aspects of gravitation


1. Zonal distribution of comets


The inclinations of comets with regard to the plan of the Ecliptic are distributed randomly. The histogram of the inclinations of the comets with regard to the equatorial plan of the Sun, shows that the direct elliptic comets are not distributed randomly, but in zones. The retrograde comets are in the gaps of the direct elliptic comets distribution.


Comet Orbits being practically plane, comets cross a number of Sun zones increasing with the inclination of their orbit with regard to the equatorial plan of the Sun. For this reason, the zonal effect is observable only for inclination not greater than 30°. Over that inclination, comets are changing too often of zone while turning around the Sun, so that the zonal effect is completely disturbed.


There are practically no comets and no asteroids or planets as well in the close vicinity of the equatorial plan of the Sun.


1 : TEMPLE-TUTTLE                                                        2 : HALLEY


The zonal distribution of comets


in X-coordinate: the inclination of the orbital plan of comets with regard to the equatorial plan of the Sun

in Y-coordinate: the number of elliptic comets per interval of 1°

2. Zonal winds of gaseous planets


Zonal winds have been observed, for a long time now, at the surface of gaseous planets.






(continuous curve: Jupiter, dotted curve: Saturn)


Zonal Saturn and Jupiter winds (VOYAGER satellites probes)

3. Oceanic currents


The Atlantic Ocean, the Indian Ocean and the Pacific Ocean are animated by a direct equatorial current, W/E direction, therefore in the direction of rotation of the Earth. They also have two tropical opposite currents each side of the previous one, then two direct moderate currents. Finally there are two polar direct currents. That of the Antarctic is perfectly well defined. Its flow very largely exceeds the 40 million m3/s.


There would be thus three zones well identified in the Northern Hemisphere against two in the Southern Hemisphere


The nature of the Arctic and Antarctic currents ruins any attempt of thermal explanation of the oceanic currents. The temperature is constant. Salinity, and thus the density, cannot explain this phenomenon either. It is also constant throughout this current.

4. Other phenomena linked to the zonal effect of gravitation


4.1 Equatorial plane of the Sun  (for comets  see § 1)


All the planets are in the vicinity of the equatorial plane of the Sun. This is the case of the Earth.

This phenomenon has no explanation recognised by the entire scientific community.


Poincaré published in 1901 (Poincaré, Œuvres mathematiqes © Gauthier-Villars, 1951 Volume VII p 41 to 217) important papers on the rotating fluid masses. He highlighted, mathematically, the appearance of flattened figures in condensing and rotating fluids. This phenomenon has been mentioned several times on a qualitative point of view to explain the equatorial concentration of bodies. Yet the complex studies of Cournot (addition to the translation of the System Herschel, on the distribution of cometary orbits) seem to show, a gap for the Sun system body inclinations compared with the Gaussian distribution.


4.2 Galaxies


All stars are in the vicinity of the main plane of galaxies. This phenomenon has no explanation recognised by the entire scientific community.


4.3 The rings of Jupiter, Uranus, Saturn and Neptune


This phenomenon remains unexplained.


4.4 The Sun and the planets turn around themselves. Their rotation speed on themselves decreases with latitude. (for gaseous planets see also §2).


This phenomenon remains unexplained.










Le champ magnétique


faisceaux cathodiques







Electron beams

magnetic field















 May 2000.

This report is public. Its use as a whole or the use of any part thereof cannot involve any subsequent right.

Ce rapport n'est couvert d'aucune protection. Son utilisation, en tout ou partie, ne peut générer aucun droit.


1 Introduction


Des électrons peuvent être en translation sans champ magnétique. Dans les directions observées, à un instant donné, le champ existe seulement lorsque le tube cathodique est orienté dans un sens, il n'existe pas dans l'autre sens.


Quelle que soit la cause de la disparition du champ, la présente note montre que le champ magnétique d’un faisceau d’électrons ne peut en aucune manière résulter de la translation des électrons.


L’analyse de la cause de la disparition du champ magnétique des faisceaux d’électrons fait l’objet n’une note séparée.




1 Introduction

Electrons might have a motion of translation without having any magnetic field. For each direction of measurements, at a given time, the magnetic field exists only in one way but not in the opposite way.


Whatever is the root cause of the cancellation of the magnetic field, this report establishes that the magnetic field of electrons can, in no way, be a result of their motion of translation.


The root cause analysis of the magnetic field cancellation is included in another report.




2. Dispositif expérimental

Le tube cathodique utilisé est un tube de Perrin modifié en sorte que les bobines du capteur soient le plus près possible du faisceau. La partie sphérique du tube d’origine a été remplacée par un tube en pyrex de 40 mm de diamètre.


La tension d’anode est de +400V en crête, redressé deux ondes, mais non filtré, en sorte que le courant induit dans le capteur soit détectable par un convertisseur analogique numérique après une amplification de facteur 200 ; l’ordre de grandeur de la tension mesurée est de 10mV. La tension d’anode est maintenue tout au long des mesures. L’arrêt du faisceau est obtenu en coupant le chauffage de la cathode. Le chauffage est alimenté en 10 V redressé 2 ondes et filtré.


Le capteur est constitué de 12 bobines de 1300 spires chacune montée en série et débitant sur une résistance de 1MW connectée à un amplificateur opérationnel monté en sorte que le facteur d’amplification est de 200.


Le signal délivré est envoyé sur le convertisseur analogique-numérique d’un module d’acquisition connecté au port parallèle d’un PC.


2. Device description

The cathodic tube used is a Perrin’s tube modified so that the sensor coils are the nearest as possible from the cathodic beam. The spherical part of the tube has been replaced by a pyrex tube 40mm diameter.


The tube anode is at up to +400V to crest, 50Hz,  two waved rectified, but not filtered, so that the modulated magnetic field of the beam might be detected by the sensor after amplification factor of 200. The order of magnitude of the signal delivered to the analogic-digital converter is 10 mV. The anode voltage is maintained throughout the measurements. The electron beam is stopped by switching off the cathod heating. The cathod heating is powered by a 10V two waves rectified and filtered current.


The sensor is made of 12 coils 1300 loops each. The sensor is connected to a 1MW resistance and to an operational amplifier mounted in such a way that the amplification factor is 200.


The signal is then delivered to an analogic-digital converter of the data acquisition module connected to the parallel port of a PC.



3. Faits observés

Les résultats obtenus sont présentés dans le tableau ci-dessous. Les mesures ont été faites dans deux directions : Nord-Sud et Verticale et dans chaque direction le tube a été successivement orienté dans un sens puis dans l’autre (vers le Nord puis vers le Sud, vers le haut puis vers le bas). Le sens correspond au sens de déplacement des électrons entre le canon et la cible. Dans chaque sens, deux mesures ont été réalisées. Les valeurs indiquées sont les nombres d’occurrences de tensions supérieures aux valeurs indiquées colonne de gauche dans les 1000 points enregistrés.




3. Observations made


The results obtained by the associated engineers are given in the table below. Two directions were used : North-South and vertical and in each direction the tube was oriented towards the two opposite ways, (ie North then South, up then down) the ways referring to the cathodic beam from the gun to the target. Two measurements were performed in each way for the related direction. The values given by the table are the number of occurences of voltage higher than the values of the left hand column, among the 1000 aquired values.




1ère mesure horizontale Nord Sud

1st horizontal measurement North South


2 ème mesure horizontale Nord Sud

2nd horizontal measurement North South


fais vers Nord 1

nul vers Nord 1

fais vers Sud 1

nul vers

Sud 1



fais vers Nord 1

nul vers Nord 2

fais vers Sud 2

nul vers

Sud 2


Beam towards North 1

w/o Beam towards North 1

Beam towards South 1

w/o Beam towards South 1



Beam towards North 1

w/o Beam towards North 2

Beam towards South 2

w/o Beam towards South 2

>17 mV






>17 mV





>16 mV






>16 mV





>15 mV






>15 mV





>14 mV






>14 mV





>13 mV






>13 mV





>12 mV






>12 mV

















1ère mesure verticale

1st vertical measurement



2ème mesure verticale

2nd  vertical measurement


fais vers Haut1

nul vers Haut 1

fais vers Bas 1

nul vers Bas 1



fais vers Haut 2

nul vers Haut 2

fais vers Bas 2

nul vers Bas 2



up 1

w/o beam up 1


down 1

w/o beam

down 1




up 2

w/o beam up 2


down 2

w/o beam

down 2

>17 mV






>17 mV





>16 mV






>16 mV





>15 mV






>15 mV





>14 mV






>14 mV





>13 mV






>13 mV





>12 mV






>12 mV
















nota: fais = avec faisceau (cathode chaude); nul = sans faisceau (cathode froide)

note :beam= with electron beam (hot cathod) ; w/o beam = without electron beam (cold cathod)




4. Conclusion.


Le bruit de fond résulte essentiellement du champ magnétique du circuit de mise sous tension de l’anode et dépend donc de la position des cables qui changent en fonction de la position du capteur fixé au tube cathodique.


Le champ magnétique qui résulte du circuit de chauffage de la cathode est très largement inférieur au seuil détectable par le capteur. A titre indicatif, le champ magnétique résultant du circuit de mise sous tension de l’anode +400V est lui-même indétectable lorsque le courant est filtré au lieu d’être simplement redressé deux ondes.


Le champ magnétique du faisceau cathodique est en phase avec le bruit de fond à 50 Hz.


On constate que l’écart entre les signaux mesurés avec faisceau et sans faisceau dépend de l’orientation du tube. Il est pratiquement nul lorsque à l’heure de mesures, le faisceau est dirigé vers le bas et vers le Sud.


Il est maximal lorsque le faisceau est dirigé vers le haut et vers le Nord.






4. Conclusion

The background noise results mainly from the magnetic field the anode voltage circuit, and thus depends upon the cable routes which are modified when changing the tube and sensor position.


The magnetic field associated to the cathod heating is several orders of magnitude lower than the sensor threshold. This is confirmed by the fact that the magnetic field of the anode circuit is not detected by the sensor when the related current is not only two waves rectified but also filtered.


The gap between the signals measured with electron beam and without electron beam is nearly nul when the beam is either oriented downwards or towards the South.


This gap is maximum when the beam is oriented either upwards or towards the North.





4. Conclusion (suite).

Il n’est pas concevable qu’un champ magnétique de 50 Hz, de signe contraire à celui du faisceau, apparaisse au moment de la mesure avec faisceau, le seul changement entre les mesures étant la mise en route du chauffage de la cathode, mais bien plus qu’il n’apparaisse que dans un sens dans les deux directions utilisées.


En conséquence, il existe des orientations de l’Espace dans lesquelles, à un instant donné, les faisceaux d’électrons n’ont pas de champ magnétique alors que leur mouvement de translation n’est en rien modifié par rapport aux autres orientations.


Le champ magnétique des électrons ne peut donc en aucune manière résulter de leur translation dans l’Espace.


La seule autre variable connue étant leur moment magnétique, et en conformité avec les rapports précédents des ingénieurs associés, il est donc établi que le champ magnétique des électrons résulte exclusivement de leur moment magnétique. L’équation de Maxwell-Ampère est donc fausse et il ne saurait y avoir le moindre problème de mouvement relatif dans les phénomènes électromagnétiques.



4. Conclusion  (continued)

It cannot be imagined how a 50 Hz magnetic field opposite to the beam magnetic field, could appear just when the magnetic field of the beam is measured as the only change is the switching on of the cathod heating. Moreover the magnetic field should only appear in one way of the selected directions.


As a consequence, there are orientations within Space where, at a given time, the electron beams have no magnetic field although their translation motion is not modified compared with the other orientations.


Thus the magnetic field of electrons can in no way be a result of their translation motion in Space.


The sole known other variable is their magnetic moment. So that, in compliance with all the previous reports of the associated engineers, it is now clearly established that the magnetic field of electrons is only a result of their magnetic moment. Therefore the Maxwell-Ampere’s equation is definitively wrong. As a result, there is not the slightest problem of relative motion within the electromagnetic phenomena.















The electron intrinsic magnetic field


is not a dipole.



The Rowland effect.















April 2016





The magnetic field of a conductor crossed by a current of 0 to 2.5 A, rotating at speeds between 100 and 260 revolutions per second is five to fifteen times higher than that produced by a current of the same intensity in the motionless conductor.


The electrons are rotating with the conductor. The magnetic field results from the Rowland effect. But if the magnetic field of the rotating electrons was likened to the field of a loop, it could not be detected by measuring coils which are parallel to the conductor.


Thus, this magnetic field can only result from the intrinsic magnetic field of the electrons aligned in the conductor axis by precession effect.


But the position of the coils relative to the conductor does not allow to detect dipole fields. The coils can measure the rotational magnetic field of a variable current, but can not detect a variable dipole field.


It is therefore necessary that the magnetic field of the electron has a rotational structure that can be measured by the coils.



The conductor is a copper tube 4 mm OD diameter and 280mm long, fixed at its ends to two steel rods of 3 mm diameter. One of the rods has a length of about 700 mm and is guided by three ball bearings inserted in a 10 mm ID diameter support tube. An electric motor 12 VDC, 25 A 15600 RPM is fixed to the other end of the rod and fixed to the support tube. The other rod 50 mm long, is guided by two ball bearings. The two steel rodss are fixed to the copper tube by insulating connectors. The current is delivered to the conductor by carbon contacts maintained by springs.

The power supplies are located more than one meter from the device. The motor itself is 700 mm from the sensor located in the middle of the rotating tube.


The motor speed is measured by an UV door: 12.81 Hz for 20 wave lengths: 256 Hz.




The magnetic field of the pulsating current at 100 Hz passing through the rotating tube is of the order of 10E-7 Tesla. It is measured by a sensor with two coils in series situated on either side of the rotating tube and contained in its plane.

Both sensor coils consist of approximately 1200 turns of copper wire 0.1 mm diameter.


The sensor signal is sent to an integrated linear amplifier AD 820 The gain is 200. The offset is not corrected. The amplifier is supplied with +15 V regulated monopolar.


The rotating tube is supplied with 9V AC rectified but not filtered. This results in a pulse at 100 Hz of the current in the tube. This pulse induces a voltage in the sensor coils. The sensor can not distinguish the direction of the magnetic field as the variation of the inductor current sign changes at each half period. The amplifier allows only positive changes to allow measurement with a voltmeter.


The amplified signal is measured by a digital voltmeter. It is also sent to a digital to analog converter connected to a USB port of a computer with a digital oscilloscope.

This curve shows the voltage delivered by the coils measured after amplification as a function of the current in the motionless conductor.



The voltage is measured after the amplifier for the intensities of 0, 1 and 2A. Measurements were replicated dozens of times in each direction of rotation and each direction of the current in the conductor.


In the absence of current, the rotation produces no magnetic field.


The starting and stopping the motor as well as the power supplies needed for the experiment cause no voltage measured after the amplifier when the conductor is not crossed by any current.


The intensity drop in the conductor resulting from the rotation is about 0.5 A corresponding to the increase of the contact resistance.


Instead of falling in proportion to the drop in intensity of the current in the rotating tube, there is a very significant rise of the magnetic field measured by the sensor.


The field is three to seven times higher than the field of the same current in the motionless conductor.






The rotating conductor has been shortened to 140 mm in order to reduce the vibrations and enabling measuring the rotation speed. The rotation speed was much higher than in the previous configuration. It reached 256 revolutions per second. The field is fifteen times higher than the field of the same current in the motionless conductor.

In this configuration, the sound frequency of the device is more than twice that with the first conductor 300 mm long. The speed should then be less than half; say one hundred revolutions per second. This speed is confirmed by the fact that the current in the motor increases from 10 to 20 amps. Under these conditions, the magnetic field would be proportional to the rotational speed of the conductor.


The vibrations were still significant so it was not possible to verify systematically the effect of the rotational speed on the magnetic field with this device.




The Tolman-Stewart effect that occurs when the rotation is sharply set on or off can not be the cause of the observed phenomenon since it is permanent. Moreover, the magnetic field that would be created by the rotation of the electrons with the conductor can be likened to the field outside of a solenoid of infinite length, so there is virtually zero.


The conductive tube is made of copper and is thus not magnetic. It can not therefore be a Barnett effect.


In addition, in the Tolman-Stewart effect as in the Barnett effect the magnetic field is found to be in the axis of the conductor. The sensor can not detect such a field.


It can only be a Rowland effect. The rotation of the electrons around the conductor axis causes a magnetic field. This phenomenon is the cause of the very large increase of the magnetic field of the rotating conductor.


This effect obviously depends on the direction of rotation, but the current in the conductor being rectified two phases and the sensor amplifier being supplied with monopolar voltage, there is always an increase of the induced voltage with the same sign.


This phenomenon would result from the rotation of the electrons with the conductor like loops and as a result of small translations causing a magnetic field.


However, this explanation of the Rowland effect by translation of electrons is impossible. The field would be coaxial to the driver and could not be detected by the sensor.


It is therefore a phenomenon of precession of the axis of rotation of the electrons. It results from the Coriolisacceleration. A body rotating around an axis and set rotating around another axis has its own axis of rotation pushed toward the axis of the rotation imposed.


But in the context of current theories, the magnetic field of the electron has a dipole structure.


However, the position of the coils relative to the conductor does not allow detecting dipole fields. Depending on the orientation of the dipole, the field lines traverse the coils either in opposite directions and the induced currents cancel or they do not pass through at all.





































It is therefore necessary that the magnetic field of the electron has a rotational structure to be measured by the coils.

The Rowland effect can not result from the transition of electrons as we have seen. The translation of electrons can not be the cause of the magnetism of the electric currents

The magnetic field of electric current thus results directly from the intrinsic magnetic field of electrons. Their field is oriented in the conductors so that the conductor produces a resultant magnetic field.


The old approach of electromagnetic theory, attempting to justify the Biot and Savart law by a formal analogy with Coulomb's law could not hide the lack of experimental evidence.


The axiomatic approach has been clarified. The most recent books took as its starting point the postulate of the magnetic force between two moving charges.


Unfortunately, not only this assumption obviously has no experimental justification, but it now seems completely contrary to experiment.





As a consequence, the magnetic field of the electrons can not be directly the cause of the magnet fields.


The magnetic field of the paramagnetic, diamagnetic, ferromagnetic, anti-ferromagnetic and ferrimagnetic bodies has an overall topology orthogonal to the conductors field. The only structure allowing for constituting such a topology with the elementary magnetic moments is the Helmoltz torus. A similar structure is obtained with a loop or a solenoid in the case of conductors.


It must therefore be concluded that magnetism of magnets and of bodies mentioned above, results from the existence in matter of magnets of such structures whose orientation conditions can account for different types of magnetism.


It is necessary that the electrons are organized into rings structures in the matter of magnets.


Electrons of magnets include in such structures generate a magnetic field similar to that of the magnets.







The Maxwell-Ampere equation is false. There is not any vector relationship between the magnetic field of the electrons in an electric field, so in translation, and the current vector J. There is only a formal coincidence. The magnetic field of the current is proportional to the average magnetic intrinsic magnetic field of electrons itself proportional to the electric field in the conductor.


However, the current is itself proportional to the same electric field. But the quantities have nothing to do with each other. And primarily, a Galilean reference frame change does affect neither the electron intrinsic magnetic field, nor the angular momentum.


If the charge must of course be conserved, even under varying conditions, the direct relationship between the magnetic field and the current vector is false as we have just seen. The magnetic field of electrical current is the geometric sum of the magnetic fields of electrons in the conductor. Without potential difference, so without an electric field in the conductor, the magnetic fields of electrons are distributed randomly and the conductor has no magnetic field.


An electric field in the conductor directs the rotational magnetic field of electrons so that the driver has himself a rotational magnetic field. Thereby by dissociating the direct link between the current vector and the magnetic field, we introduced the ability to show a magnetic field variation of the electric field without the conservation of charge is questioned. The problem of the Ampere equation in variable regime is therefore moot.


The displacement current Maxwell added to the Ampere equation to cancel the mathematical divergence of the current in variable regime and meet the conservation of charge, has now a very simple physical explanation. It is simply the magnetic field resulting from the magnetic field of electrons that do not enter into the current J. For example, in the case of electrons that move transversely in a sudden enlargement of a conductor. They produce a transverse electric field that orients accordingly their magnetic field. Moreover, the equations are very similar in the case of the sudden enlargement of a pipe in fluid mechanics.

This is also the case of magnetic fields which appear when you load capacitors. The electric field in the plates themselves is zero, and therefore produces no magnetic field. But during charging, electrons are accumulating in the plates and cause a momentary additional electric field which orients their magnetic field.


The magnetic field of the electric currents result directly from the rotational magnetic field of electrons. This field is totally invariant in a Galilean reference frame change.


The problem of relative motion does not exist in electromagnetism.









Baigrie, B.                 Electricity and Magnetism: A Historical Perspective. Greenwood Press. (2006).

Bernard Pr. M.Y.      Initiation à la mécanique quantique                Editions Hachette (1960)      

Hennequin Pr. J.      Electromagnétisme et relativité restreinte.       Editions Dunod (1970)       

Keithley, J.F.             The Story of Electrical and Magnetic Measurements: From 500 B.C. to the 1940s                                        IEEE Press. (1999).

Landau Pr. L.           Théorie des champs                                                         Editions Mir, Moscou (1966)

Liboff Pr.R.L.            Introductory Quantum Mechanics                           Holden-Day Inc (1908) 

Mach Pr. E.               De la connaissance et de l'erreur                             Editions Flammarion (1908)    

Pérez Pr.J.P.& alt     Electromagnétisme                                              Editions Masson (1997)       

Tonnelat Pr. M.A.    Histoire du principe de relativité                                Editions Flammarion (1971)