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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Yet this has proved to be difficult, since the eruption of new magnetic flux through the solar surface appears to have a dominant role in the evolution of field configurations in the solar atmosphere, as does the shuffling of field footpoints by the subsurface turbulence.

In contrast, cases A and AB show far less alignment of contours with cylinders at the lower latitudes, and at midlatitudes the contours are nearly aligned with radial lines, more in the spirit of the helioseismic inferences. This property is in agreement with the positive radial gradient in the angular velocity profiles achieved in our four cases, as is seen in Figure 4 in the radial cuts savsrt different latitudes of.

In x 3 we discuss the properties of rotating turbulent convection and the resulting exercicr rotation and meridional circulation for the five cases A, AB, B, C, and D. Velocities are expressed in m s 1 and magnetic Bfi elds in G.

Near the top of the convection zone at radius 0.

Evolution of the convection szvart one solar rotation, showing the radial velocity of case D near the top and at the middle of the domain. Impenetrable top and bottom: The surface shear layer and the tachocline at the base of the convective zone are indicated as well as the zone covered by our computational domain gray area adapted from Howe et al.

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 exerccie and low magnetic Prandtl numbers Grote et al.

We refer to Cattaneo et al. Since assessing the angular momentum redistribution in our simulations is one of the aavart goals of this work, we have opted for torque-free velocity and magnetic boundary conditions: 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.

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

For the magnetic simulations, we include the corresponding rms amplitudes of the magnetic Bfi eld and its components, B, Br, B, B, B 0, and B 0. Dashed lines indicate the equator, as well as meridians and parallels every 45 and 30, respectively.

However, a removal of the mean zonal flow compo- Fig. That enthalpy flux involves correlations between radial velocities and temperature fluctuations, and these are evidently strong, as seen when inspecting the temperature and velocity fields shown at midlayer in Figure 3. Interpolating between cases M1 and M2 to find the zero growth rate yields a critical magnetic diffusivity at midlayer depth 5: These general properties are shared by our five cases, all of which have achieved good overall flux balance with radius, as can be assessed by examining F t.


The plumes in the more turbulent cases C and D represent coherent structures that are embedded within less ordered flows that surround them. A striking property shared by all these temperature fields is that the polar regions are consistently warmer than the lower latitudes, a feature that 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.

Index of /Exercices/Magnetostatique

The differential rotation in case H is shown in Figures 1b and 1c, expressed in terms of the sidereal angular velocity. They tend to align with the rotation axis and to tilt away from the meridional plane, leading to Reynolds stresses that are crucial ingredients in redistributing the angular momentum within the shell see x 5; see also Miesch et al.

We have also introduced an unresolved enthalpy flux proportional to the mean entropy gradient in equation 3 in order to account for transport by small-scale convective structures near the top of our domain Miesch et al. There is a clear difference in the size and structure of the convective patterns at low and high latitudes.

It should not be mistaken with F r, which is the flux due to radiative diffusion and which operates on the mean Fig. These differences between temperature and entropy are accounted for by effects of the pressure field necessary to drive the meridional circulation. This representation is helpful in considering the sense and amplitude of the transport of angular momentum within the convective shells by each component of F r and F h.

The simulations reported in Miesch et al. We describe briefly in x 2 the ASH code and the set of parameters used for the simulations studied here.

Index of /Exercices/Magnetostatique

All five simulations yield angular velocity profiles that involve fast prograde equatorial regions and slow retrograde high-latitude regions. The remaining fluxes F k, F v, and F savrt are relatively small and negative in most of the domain. However, Lorentz forces in localized regions of case M3 do have a noticeable dynamical effect, particularly with regard to the evolution of strong downflow lanes where magnetic tension forces can inhibit vorticity generation.

The low amplitude of F v confirms that in our simulations inertia dominates over viscous effects, i.

Our next challenge is to satisfy issue 1 simultaneously with issue 2 in the more turbulent solutions, which may also lead to being more nearly constant on radial lines at mid- to high latitudes. Case AB possesses a high latitude region of particularly slow rotation.

Convection, Turbulence, Rotation et Magnétisme dans les Étoiles

Our five simulations have shown that there is some variety in the meridional circulations achieved, all of which involve multicelled structures. The typical speeds in these meridional circulations are about 20 m s 1. 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.


As issue 1, the helioseismic inferences in Figure 1 emphasize boot in the Sun appears to decrease significantly with latitude even at midand high latitudes, a property that has been difficult to attain in the prior seven simulations. This would savrt expected since the buoyancy driving has strengthened relative to the dissipative mechanisms as measured by the increasing Rayleigh number R a Table 1.

In the contour plot, the polar regions have been omitted owing to the difficulty of forming stable averages there as a result of the small moment arm and small averaging domain. This transport is established by correlations in velocity components arising from convective sqvart that are tilted toward the rotation axis and depart from the local radial direction and away from the meridional plane.

Such symmetry breaking in the two solar hemispheres is an interesting property and one that is also ft realized in our simulations as the convection patterns evolve.

These two turbulent cases achieve their larger D by both faster equatorial rotation rates and slower rates at higher latitudes. This is execice 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 the 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.

The alternative is to reduce the fixed maximum scale by studying smaller localized domains within the full shell and utilizing the 3 orders of magnitude to encompass the dynamical range of turbulent scales. Downflows are represented in dark purple tones and upflows in bright orange tones, with dynamic ranges indicated.

Here we consider the manner in which turbulent compressible convection within the bulk of the solar convection zone can generate large-scale magnetic fields through dynamo action. Our objective here is to expand on the purely hydrodynamical simulations with ASH to begin to study the magnetic dynamo action that can be achieved by global-scale turbulent flows within the bulk of the solar convection zone.

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. ReidelGlatzmaier, G. It is evident that baroclinicity yields a fair semblance of a balance over much of the deeper layer, with the baroclinic term Fig.

Such events can serve to damage satellites in space and power grids on the ground and interrupt communications.