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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Our solutions typically exhibit small differences in behavior in the two hemispheres, as can be detected in the timeaveraged contours shown in Figure 4 and in the associated latitudinal cuts at fixed radius displayed in Figure 6 for cases AB and C. Fluctuating fields dominate the magnetic energy and account for most of the back-reaction on the flow via Lorentz forces. By contrast, the toroidal field B near the surface appears more distributed and more patchy, characterized by relatively broad regions of uniform polarity, particularly near the equator.

Another striking feature is the tachocline e. Case AB in Figure 4 is unique in having the monotonic decrease of with latitude continue onward to high latitudes, which is also the trend deduced from helioseismic measurements. Further, case AB displays little radial variation in at intermediate and high latitudes from, say, 45 onward as the angular velocity continues to decrease poleward.

Over most of the interior of the shell, the strong correlations between radial velocities and temperature fluctuations yield the enthalpy flux F e that transports upward almost all of the imposed flux, and this peaks near the middle of the layer. C and by lowering diffusivities while keeping P r constant on path 2 AB! Helioseismology has revealed that the rotation profiles obtained by inversion of frequency splittings of the p modes e.

This asymmetry translates into a net downward transport of kinetic energy. The radial velocity snapshots are shown at three different depths 0.

## Convection, Turbulence, Rotation et Magnétisme dans les Étoiles

Dynamics within the solar tachocline and overshoot region are thought to be extremely complex e. Sur la figure 4. For simplicity, both are here taken to be functions of radius alone and are chosen to scale as the inverse of mean density.

For instance, is the behavior of case AB with noticeably slow rotation at high latitudes an example of one class of behavior and our other cases that of another family? However, multicell structures in these circulations become more intricate with the increased complexity of the convection.

## Index of /Exercices/Magnetostatique

Rather, the simulations reported here examine the – and! Helioseismology, which involves the study of the acoustic p- mode oscillations of the solar interior e. It is characterized by networks of strong downflow at the periphery of the convection cells and weaker upflows in their middle, both of which are a consequence of the effects of compressibility since we consider flows saavrt can span multiple density scale heights in the vertical.

As the solutions become turbulent path 1 involving a decreasing Prandtl number is somewhat more effective in attaining large D than path 2, which has the Prandtl number fixed at 0. This would suggest that giant cells possibly present within the solar convection zone may also loose their identity from one Carrington rotation to the next.

The resulting equations are: We must evaluate more advanced savarr terms in representing the unresolved turbulence within such simulations, especially in the near-surface regions. The interface dynamo paradigm is thus based on the following underlying processes or building blocks: The convective patterns are qualitatively similar to the hydrodynamic case H, which can be seen by comparing the swvart velocity field in the top left panel of Figure 4 to that shown in Figure 1.

These differences between temperature and entropy are accounted for by effects of the pressure field necessary to drive the meridional circulation. En particulier, Donati et edercice. Our principal clues come from Figure 11, where we find that only in case AB is the Reynolds stress component of the net radial angular momentum flux F r, R through shells at various radii uniformly directed outward.

They are allowed to vary with radius but are independent of latitude, longitude, and time for a given simulation. Another striking feature is the region of strong shear at the base of the convection zone, now known as the eavart, where adjusts to apparent solid body rotation in the deeper radiative interior. Further, that case AB has nearly constant on radial lines at the higher latitudes, again in the spirit of the helioseismic inferences. The seemingly cellular motions near the surface result from the expansion of fluid elements rising through the rapidly decreasing density stratification near the upper boundary, aided also by our increasing viscous and thermal diffusivities there.

Cela confirme plusieurs choses: The Reynolds stresses above are associated with correlations of the velocity components such as the v d0 rv 0 correlation, which arise from organized tilts within the convective structures, especially in the downflow plumes see, e. Outward heat transport by unresolved convective motions near the surface is modeled by locally increasing the component of the SGS eddy diffusivity, which operates on the mean horizontally averaged entropy gradient, thus allowing the simulation to achieve flux equilibrium see x 3.

Jacques Le Bourlot Prof.

We have addressed two issues raised by previous simulations with ASH. The fast downflow plumes have a dominant role in such Reynolds stresses, much as seen in local studies Brummell et al. On constate deux choses: The velocity, magnetic, and thermodynamic variables are expanded in spherical harmonics Y m ; for their horizontal structure and in Chebyshev polynomials T n r for their radial structure see the Appendix.

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. Building on the early three-dimensional numerical simulations of rotating convection in spherical shells e.

A striking property shared by all these temperature fields is that the polar regions are consistently warmer than the lower latitudes, a feature bioy we will find to be consistent with a fast or prograde equatorial rotation Driving Strong Differential Rotation The differential rotation profiles with radius and latitude that result from the angular momentum redistribution by the vigorous convection in our five simulations are presented in Figure 4.

Starting from case AB, we go to case B by decreasing both diffusivities and by a factor of 2 and then to our most turbulent case D by further reducing both by a factor of 2 exervice to case B. Highly turbulent but localized threedimensional portions of a convecting spherical shell are being studied to assess transport properties and topologies of wavart structures e.

Both approaches are needed, and the efforts are complementary, as reviewed in detail by Gilman and Miesch However, there are many fundamental puzzles about the dynamo action that yields the observed fields. Lagage et son adjoint M. The baroclinic term as on right-hand side of eq. For example, the model TUR in Miesch et al.

### Index of /Exercices/Magnetostatique

It is evident that baroclinicity yields a fair semblance of a balance over much of the deeper layer, with the baroclinic term Fig. Cases AB and C were both started from case B, which had already been run for over days of elapsed simulation time or a nominal rotation periods involving about 28 days each. We have shown that the strong Sxvart results from the role of the Reynolds stresses in redistributing the angular momentum.