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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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. This is particularly evident in some of the downflow structures identified near the equatorial region in the upper sequence, with features labeled 1 and 2 illustrating the merging of two downflow lanes and feature 3 niot typical distortion of a lane that also involves both a site of cyclonic swirl in the northern hemisphere and another that is appropriately anticyclonic in the southern hemisphere.

Instabilities driven by shear and magnetic buoyancy further influence the structure and evolution of the tachocline and likely play an important role in the solar activity cycle.

In either scenario, there is separation in the sites of generation of toroidal field in the strong shear of the tachocline and regeneration of poloidal field either near the surface or in the bulk of the convection zoneyielding what is now broadly called an interface dynamo Parker The computational domain extends from 0: We turn in Figure 12 to an exercicf of case Exericce in terms of how well a simple thermal wind balance is achieved or violated. The angular velocity profile in such simulations is generally sensitive to the parameters of the problem, and more solar-like profiles such as case H can be achieved by varying the Reynolds and Prandtl numbers in particular Elliott exwrcice al.

L identification d un cycle de giot ans des taches solaires, s accompagnant d un ren.

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

On path 1 in going from case A to case C via case B, we incrementally decreased the eddy viscosity while keeping the eddy diffusivity constant, thereby reducing the Prandtl number P r by a factor of 8. The anelastic approximation captures the effects of density stratification without having to resolve sound waves, which would severely limit the time step. The southern hemisphere has likewise poleward flow near the top at low latitudes, with ascending motions again present from the equator to about 20 latitude.

Helioseismology, which involves the study of the acoustic p-mode oscillations of the solar interior e. Case H is well evolved, with a complex convective structure and a solar-like differential rotation profile x 3. It begins in hydrostatic balance so the bracketed term on the right-hand side of equation 3 initially vanishes. Further, since the fluid is electrically conducting, currents will flow and magnetic fields must be built.

## Index of /Exercices/Magnetostatique

Chapitre 3 et Appendice A. We have shown that the strong D results from the role of the Reynolds stresses in redistributing the angular momentum. They often tend to produce mean fields of a dipolar nature, although quadrupolar configurations are preferred in some parameter regimes, generally characterized by high Rayleigh numbers and low magnetic Prandtl numbers Grote et al.

This has the consequence that all our spherical shells possess fast prograde equatorial rotation relative to the reference frame.

Comparison of this with the radial and latitudinal rms velocities reveals that all possess very comparable amplitudes, suggesting fairly isotropic convective motions near the midplane. Such downward transport of angular momentum is well compensated by the two other terms F r, R and F r, M, having reached a statistical equilibrium of nearly no net radial flux, as can be seen by noting that the solid curve F r is close to zero.

The resulting axisymmetric meridional circulation is maintained by Coriolis forces acting on the mean zonal flows that appear as the differential rotation, by buoyancy savarg, by Reynolds stresses, and by pressure gradients.

### Index of /Exercices/Magnetostatique

We have so far sought to address some of these questions by perturbing the evolving solutions to see if they might flip to another state, but they have not done so. We have achieved in one case the slow pole behavior comparable to that deduced from helioseismology and have retained in our more turbulent simulations a consistently strong D.

The color table is as in Fig. The contour plots reveal that there are some differences in the realized in the northern and southern hemispheres, although such symmetry breaking is modest and probably will diminish with longer averaging.

The time evolution is carried out using an implicit, second-order Crank-Nicholson scheme for the linear terms and an explicit, secondorder Adams-Bashforth scheme for the advective and Coriolis terms. This sampling does not capture more localized features such as vertically aligned vortex tubes, which can be seen on higher resolution images but occur on scales smaller than the sampling grid.

They are able to maintain their identity, although with some distortion and mobility, over significant intervals of time. The largest current three-dimensional turbulence simulations can savaft about 3 orders of magnitude in each dimension.

We conclude that the Reynolds stresses have the dominant role in aavart the prograde equatorial rotation seen in our simulations, with its effectiveness limited by the opposing transport of angular momentum by the meridional circulation. The radial velocity snapshots are shown at three different depths 0.

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. These cells possess exerfice helicity and generally drive a large differential rotation, thus providing all the necessary ingredients for asvart -! In this paper we report simulations bilt hydromagnetic dynamo action in the solar convection zone at unprecedented spatial resolution.

We plan to examine such issues of solution uniqueness in our following studies in which we seek to extend the slow-pole characteristics of case AB to other parameter settings involving more complex convection. These downflow networks essentially represent coherent structures amidst the turbulence, and they are found to have a most significant role in the nonlinear transport of angular momentum by yielding correlations between different velocity components that form Reynolds stress terms.

Buoyancy driving within our thermal convection involves downflows that are cooler and thus denser and upflows that are warmer and lighter than the mean; there are systematic asymmetries in those temperature fluctuations, much as in the radial velocities.

Thus, breaking the Taylor-Proudman constraint that requires rotation to be constant on cylinders, equal to zero, can be achieved by establishing exerdice latitudinal entropy gradient.

Without recourse to direct simulations, the angular momentum and energy transport properties of turbulent convection have also been considered using mean-field approaches to derive second-order correlations the Reynolds stresses zavart anisotropic heat transport under ssavart assumption of the separability of scales. We are keen to also investigate aspects of the rotational shear evident close to the solar surface. Since differential rotation is a key ingredient in all dynamo models, we also examine here the nature of the rotation profiles that can be sustained within the deep convection zone as strong magnetic fields are built and maintained.

Although all of our solutions possess complicated temporal variations, our sampling in time to obtain the averaged fluxes suggest that we are sensing the equilibrated state reasonably well. At low Reynolds numbers the transition between equatorial modes and polar modes occurs savarrt the tangent cylinder.