que Vc-VA = VE-VA? EXERCICE 3 (5 points). En utilisant la loi de Biot et Savart, exprimer le champ magnétique créé, en son centre 0, par une. 2) Que permet de calculer la loi de Biot et Savart? Donner son Tous les exercices doivent être traités sur les présentes feuilles (1 à 5) qui seront agrafées à la.

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Others believe that the poloidal field is regenerated by the cumulative action of many small-scale cyclonic turbulent motions on the field throughout the convection zone, rather than just close to the surface e.

We have analyzed the transport of angular momentum in establishing such differential rotation and clarified the roles played by Reynolds stresses and the meridional circulation in this process. This behavior appears to arise from increasing complexity leading to a weakening of nonlinear velocity correlations that have a crucial role in angular momentum redistribution.

A Reynolds number based on the peak velocity at middepth would be about a factor 4 larger. Our simulations have attained a spatial resolution adequate to begin to attain coherent structures amidst the turbulence, which is believed to be a key in sustaining strong Reynolds stresses at higher turbulence levels. We plan to study aspects of symmetry breaking further with more extended simulations in the near future.

These two turbulent cases achieve their larger D by both faster equatorial rotation rates and slower rates at higher latitudes. Further, that case AB has nearly constant on radial lines at the higher latitudes, again in the spirit of the helioseismic inferences.

For simplicity, both are here taken to be functions of radius alone and are chosen to scale as the inverse of mean density.

Index of /Exercices/Magnetostatique

There was a tendency for D to diminish in some of the turbulent solutions that also required the emerging energy flux to be invariant with latitude. Cyclic solutions have been found, but field reversals are more often aperiodic, particularly for high Rayleigh numbers. Such tilting away from the local radial direction in coherent downflows has been seen in high-resolution local f-plane simulations of rotating compressible convection Brummell et al.

We also refer to Hathaway savatt al. We have extended our already well-tested hydrodynamic ASH code see Clune et al.

From having examined in detail angular momentum flux stream functions not shown with radius and latitude consistent exrrcice equations 7 9we observed that the Reynolds stress contributions to such transport possessed multicelled structures with radius at high latitudes in all the cases except case AB.

Table 2 summarizes various rms velocities that characterize our five simulations as bior in the middle of the layer where the enthalpy flux also peaks. If the simulation were in a thermally relaxed state, the total flux through safart horizontal surface would be constant and equal to the solar luminosity that is applied at the upper and lower boundaries: The time evolution is carried out using an implicit, bioh Crank-Nicholson scheme for the linear terms and an explicit, secondorder Adams-Bashforth scheme for the advective and Coriolis terms.

We utilize the same radial profile for that mean eddy diffusivity in our five cases in order to minimize the impact of our SGS treatment on the main properties of our solutions. These structures are created somewhere below the photosphere and rise upward, bending to pierce the photosphere in the form of curved tubes.


These temperature contrasts are very small compared to the mean temperature near the top of our domain of about 10 5 K and of K near its base. The effect of closed as opposed to open boundary conditions seems to be that in the former the savarr energy amplification is more efficient, with potentially a lower dynamo threshold. As these mappings become available, they may be able to confirm or refute the multicell radial structure of meridional circulation Fig.

The boit velocity of the rotating reference frame is nhz, which corresponds savvart a rotation period of 28 days. Helioseismology has revealed that the rotation profiles obtained by inversion of frequency splittings of the p-modes e. The simulations with ASH have not yet sought to deal with questions of the near-surface rotational shear layer nor with the formation of a tachocline near the base of the convection zone.

Index of /Exercices/Magnetostatique

In a broader sense in considering all of our cases, we deduce that in the radial direction the transport of angular momentum is significantly affected by both the meridional circulation and the Reynolds stresses. Such a succession of developments from helioseismology provides both a challenge and a stimulus to theoretical work on solar convection zone dynamics.

We have shown that the strong D results from the role of the Reynolds stresses in redistributing the angular momentum. This comes about because of both advection and distortion of the cells by the mean zonal flows associated with the differential rotation here at the equator leading to relative angular displacements in longitude of about 70 over one rotation dd and fairly rapid evolution and some propagation in their individual downflow patterns Downflow Networks and Variation with Depth The convective structures as delineated by the downflow networks show distinctive changes as the level of turbulence is increased in going from case A to case D.

This can result from suitable correlations in velocity and thermal structures yielding a latitudinal heat flux that may produce substantial entropy variations at the higher latitudes, thereby leading to greater baroclinic contributions in equation 11 that define the variation of mean zonal velocity. As issue 2, there was a tendency for D to diminish or even decrease sharply within the prior simulations as the convection became more turbulent, yielding values of D that were becoming small compared to sacart helioseismic deductions.

Given that the dissipation scales are on the order of 0. Solid contours denote counterclockwise circulation and dashed contours clockwiseequally spaced in value.

Most of our cases possess overall latitudinal contrasts in that are in the realm of solar values deduced from inversion of helioseismic data, yet case Ey stands out in having the systematic decrease of with latitude extending almost to the poles, which appears to be another distinguishing feature of the actual solar profiles.

The wide range exercoce dynamical scales of turbulence present in the solar convection zone yield severe challenges to both theory and simulation: Such behavior is most interesting, and it is necessary to understand just which convective properties within case AB allow it to come into reasonable contact with the helioseismic profiles for deduced in the bulk of the solar convection zone.

All five simulations yield angular velocity profiles that involve fast prograde equatorial regions and slow retrograde high-latitude regions.


Convection, Turbulence, Rotation et Magnétisme dans les Étoiles – PDF

Whereas the overall latitudinal contrasts from equator to pole in the models and the Sun are roughly of the same order, the angular fe in the Sun continues to slow down much more as the pole bito approached. The highspeed solar wind and its energetic particles, coronal mass ejections, and explosive flares are all linked to the changing magnetic fields within the extended solar atmosphere. Given these competing processes, it is not selfevident what pattern of circulation cells should result nor how many should be present in depth or latitude.

Helioseismology has also recently detected prominent variations in the davart rate near the base of the convective envelope, with a period of 1. In cases B, C, and D, there is some alignment of the contours at the lower latitudes with dt rotation axis, thus showing a tendency for to be somewhat constant on cylinders. This subsurface region is now being intensively probed using local domain helioseismic methods, revealing the presence of remarkable large-scale meandering flow fields much like jet streams, banded zonal flows, and evolving meridional circulations, all of which contribute to what is called solar subsurface weather SSW; Haber et al.

The flows and fields exhibit substantial kinetic and magnetic helicity although systematic hemispherical patterns are only apparent in the former.

Angular velocity contours at midlatitudes are nearly radial, and the rotation savarf decreases monotonically with increasing latitude dt in the Sun. However, multicell structures in these circulations become more intricate with the increased complexity of the convection. The helioseismic probing with ring diagram methods and explicit inversions is able to sense the meridional circulations only fairly close to the solar surface, typically extending to depths of about 20 Mm or to a radius of 0.

The results have been averaged over a period of days. Rather, we find that the Reynolds stresses are the main agents responsible for maintaining the rotation profiles in our simulations see x 5 AchievvinggSustained Dynamo Action We now consider the dynamo possibilities that such intricate convective patterns and large differential rotation can lead to.

Helioseismology has revealed that the rotation profiles obtained by inversion of frequency splittings of the p modes e. As might be expected, the overall rms radial velocities listed in Table 2 increase with complexity in the flow fields in going from case A to case D. They are allowed to vary with radius but are independent of latitude, longitude, and time for a given simulation. Sur la Figure 4.

The strong latitudinal variation of angular velocity observed near the surface, where the rotation is considerably faster at the equator than near the poles, extends through much of the convection zone depth about Mm with relatively little radial dependence. Thus, we are concerned only with the central portion of the convection zone, dealing with neither the penetrative convection below that zone nor the two shear layers present at the top and bottom of it.