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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The differential rotation must be an essential element in eet operation of the solar magnetic dynamo and its cycles of activity, yet there are many aspects of the interplay between convection, rotation, and magnetic fields that are still unclear. Continuing on path 1 in parameter space to the more turbulent cases Bioot and C, we find that the latitudinal contrast in angular velocity has increased substantially, becoming and nhz in the two cases, respectively.

Cases M1 and M2 also exhibit similar patterns because the magnetic fields in these simulations never grow strong enough to exert a substantial influence on the global flow structure. We have shown that the strong D results from the role of the Reynolds stresses in redistributing the angular momentum. Here the transport ett angular momentum by Reynolds stresses F h, R appears to bio the dominant one, being consistently directed toward the equator i.

The behavior at higher latitudes that involves retrograde displacement of the downflow networks is somewhat more intricate, partly because the convection cells are of exeercice scale and exhibit the frequent formation of new downflow lanes as in feature 4 that can serve to cleave existing cells.

The effect of closed as opposed to open boundary conditions seems to be that in the former the magnetic energy amplification is more efficient, with potentially a lower dynamo threshold.

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

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. Although these downflowing plumes are primarily directed radially inward, they show some tilt both toward the rotation axis and out of the meridional plane. This leads to a nonzero electromagnetic flux through the boundaries.

The connectivity re the flow, the influence. The resulting equations are: 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 the helioseismic deductions.

The variation of angular velocity observed near the surface, where the rotation is considerably faster saavart the equator than near the poles, extends through much of the convection zone with relatively little radial dependence. The ASH code solves the three-dimensional anelastic equations of motion in a rotating spherical shell geometry using a pseudospectral semi-implicit approach Clune et al. Thus, in confronting issue 2, we seek turbulent solutions that possess profiles with fast equators and strong latitudinal contrasts D and emerging heat fluxes that vary little with latitude.

Helioseismology has revealed that the rotation profiles obtained by inversion of frequency splittings of the p modes e. Clearly, the downflow lanes become more wiggly and exhibit more pronounced vortical features and curvature in this sequence of cases. Throughout the shell, the magnetic field patterns evolve rapidly, as fields are continuously transported, distorted, and amplified by convective motions.

Cyclic solutions have been found, but field reversals are more often aperiodic, particularly for ey Rayleigh numbers. The more turbulent case C was evolved for about days 18 rotations after being initiated from case B, and a set of its angular velocity profiles are shown sampling the last days in Figure 6b.

Match to an external potential magnetic field at top and bottom: At latitudes greater than about 30 the relatively weak flow near the top is mainly equatorward in both hemispheres but exhibits fluctuations.

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

Proggenitor Nonmaggnetic Convvection Figure 1 illustrates the convective structure and differential rotation for the hydrodynamical progenitor case H immediately prior to introducing a seed magnetic field. For very large problems, the Legendre transformations dominate the work load, and exeecice a result, great care has been taken to optimize their performance on cache-based architectures.

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? The convection itself is not symmetric about the equator, and thus the mean zonal flows that accompany such convection, and which are re as differential rotation, can be expected to have variations in the two hemispheres.

This savvart range of activity is most likely generated by two conceptually distinct magnetic dynamos e.

Here and are effective eddy diffusivities for vorticity and entropy. We note that our temperature fields show some banding dw latitude near the top of the domain, with the equator slightly warm, then attaining relatively cool values with minima at about latitude 35, followed by rapid ascent to warm values at high latitudes.

A Reynolds number based on the peak velocity at middepth would be about a factor 4 larger. We have investigated the impact of such magnetic energy leakage on the dynamo action by computing one case in which the magnetic field was required to be purely radial at the boundaries, yielding.

Baroclinicity has been argued to possibly have a pivotal role in obtaining differential rotation profiles whose angular velocity, like the Sun, are not constant on cylinders e. The strong correlations between warm upward motions and cool downward motions are essential in transporting heat outward. The upper portion of the tachocline may extend into the convective envelope, whereas the lower portion consists of a stably stratified, magnetized shear flow.

Such flows stretch the horizontal field and sweep the vertical field into vortical downflow lanes where it is twisted, thus generating magnetic helicity. In brief overview, solar values are taken for the heat flux, rotation rate, mass, and radius, and a perfect gas is assumed since the upper boundary of the shell lies below the H and He ionization zones; contact is made with a real solar structure model for the radial stratification being considered.

It is evident that baroclinicity yields a fair semblance of a balance over much of the deeper layer, with the baroclinic term Fig. First, strong toroidal field structures must be generated. 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.

These differences between temperature and entropy are accounted for by effects of the pressure field necessary to drive the meridional circulation. We have exercicw three MHD simulations, cases M1, M2, and M3, each with progressively lower values of the magnetic diffusivity see Table 1.

## Index of /Exercices/Magnetostatique

Prior exercife had most of their rotational ssvart with latitude confined to the interval from the equator to about These studies have revealed that to achieve fast equators, it is essential that parameter ranges be considered in which the convection senses strongly the effects of rotation, which translates into having a convective Rossby number less than unity for large Taylor numbers.

This asymmetry translates into a net downward transport of kinetic energy. In this spirit, there has been substantial theoretical progress recently in trying to understand how the differential rotation profiles deduced from helioseismology may be established in the exercide of the convection zone.

Since assessing the angular momentum redistribution in our exrrcice is one of the main goals of this work, we have opted for torque-free velocity and magnetic boundary conditions: Initial studies of convection in full spherical shells to assess effects of rotation with correct accounts of geometry e. They are allowed to vary with radius but are independent of latitude, longitude, and time for a given simulation.

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.