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 highspeed solar wind and its energetic particles, coronal mass ejections, and explosive flares are all linked to the changing magnetic fields within the lli solar atmosphere.

## Index of /Exercices/Magnetostatique

Interpolating between cases M1 and M2 to find the zero growth rate yields a critical magnetic diffusivity at midlayer depth 5: There is further a thin shear xavart layer near the surface in which increases with depth at intermediate and high latitudes.

We first note that both the total kinetic and magnetic energies remain small compared to the total potential, internal, and rotational energies contained in the shell. Another striking feature is the tachocline exercce. Table 2 reveals a most interesting contrast in behavior for the two paths.

Li is instructive to briefly consider the exchange of energy among different reservoirs in our simulations. This yields a weak meridional component F h, M seeking to spin up the poles to the latitudinal angular momentum flux, thereby allowing the equatorward transport by the Reynolds stress component F h, R to succeed in extracting angular momentum from the higher latitudes.

The radiative flux becomes significant deep in the layer because of the steady increase of radiative conductivity with depth, and indeed by construction it suffices to carry all exercicee imposed flux through the lower boundary of our domain, where the radial velocities and thus the convective flux vanishes. Both issues may be intertwined since the rate of approach to equilibration can be influenced by the attraction characteristics of that differential rotation state and, of course, by the amplitude of the fluxes available to redistribute angular momentum to achieve that state see x 4.

C and by lowering diffusivities while keeping P r constant on path 2 AB!

Turning to case C in Figure 8b, it exhibits three circulation cells positioned radially at low latitudes, with the outermost again yielding poleward flow at the top of the domain that extends to about 35 in latitude. The circular arcs 90 encompass a hemisphere, and the rest of the globe is contained in the lunes on either side. We find that the convection is able to maintain a solar-like angular velocity profile despite the influence of Maxwell stresses, which tend to oppose Reynolds stresses and thus reduce the latitudinal angular velocity contrast throughout the convection zone.

Much of the small-scale dynamics in the Sun dealing with supergranulation and granulation are, by necessity, then largely omitted. Downflow lanes and plumes are continually advected, sheared, and distorted by differential rotation and nonlinear interactions with other flow structures.

In case AB Fig. The resulting equations are: Since assessing the angular momentum redistribution in our simulations is one of the main goals of this work, we have opted for torque-free velocity and magnetic boundary conditions: Streamlines of the mean axisymmetric meridional circulation achieved in a case AB averaged over days and in b case C averaged over days.

N r, N, and N are the number of radial, latitudinal, and longitudinal mesh points, respectively. As viewed near the top, the tendency of the convection in our laminar case A to be organized into banana cells nearly aligned with the rotation axis at low latitudes is progressively disrupted by increasing the level of complexity in going in turn to cases AB, B, C, and D.

There is evidently some symmetry breaking exercicr the two hemispheres. Dark tones in turn represent downflow, inward, and westward fields, with the ranges for each color table indicated.

This striking property of achieving a nearly constant KE along path 2 where both R e and P e increase comparably is a remarkable feature of this intricate rotating system that is currently unexplained. Our primary objective is to gain a better understanding of magnetic field amplification and transport by turbulent convection in the solar envelope and the essential role that such processes play in the operation of the solar dynamo.

Cyclic, dipolar dynamos were found by Gilman and Glatzmaiera, b for somewhat higher Rayleigh numbers, but the periods were significantly shorter than the solar exedcice cycle 1 10 yr and toroidal fields were found to propagate poleward during the course of a cycle rather than equatorward as in the Sun. All cases exhibit a prograde equatorial rotation and a strong contrast D from equator to pole.

### Index of /Exercices/Magnetostatique

In contrast, the previous models showed little variation in at the higher latitudes, having achieved most of their latitudinal angular velocity contrast D in going from the equator to about We utilize the same savaft 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.

This is a well-known difficulty in dynamo simulations within astrophysical or geophysical contexts see, e. The simulations reported here resolve nonlinear interactions among a larger range of scales than any previous MHD model of global-scale solar convection, but motions exerciice must exist in the Sun on scales smaller than our grid resolution. This would be expected since the buoyancy driving has strengthened relative to the dissipative mechanisms as measured by the increasing Rayleigh number R biit Table 1.

A striking property shared by all these temperature fields is that the polar regions are consistently warmer than the lower latitudes, a feature rt 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 exercic from the angular momentum redistribution by the vigorous convection in our five simulations are presented in Figure 4.

For all the cases, strong poleward cells are present near the surface at low latitudes as well as return flows at middepth.

This asymmetry translates into a net downward transport of kinetic energy.