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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Cependant il est prudent de calculer ces solutions sur plusieurs temps ohmiques car il peut y avoir des surprises, et des dynamos transitoires. Similarly, the low amplitude of the Poynting flux confirms that magnetic processes in case M3 do play a role in the overall energy transport but not to the point of significantly modifying the flux balance established in the nonmagnetic progenitor case H.

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.

It is encouraging that we have poleward circulations in the upper regions of the simulations, which is in accord with the general sense of the mean flows near the surface being deduced from local helioseismology, although two-cell behavior with latitude has been detected recently only in the northern hemisphere near the peak of solar activity Haber.

The angular velocity in all our cases exhibits substantial variations in time, and thus long time averages must be formed to deduce the time mean profiles of shown in Figure 4. The highspeed solar wind and its energetic particles, coronal mass ejections, and explosive flares are all linked to the changing magnetic fields within the extended solar atmosphere.

Thus, here too the Reynolds stress terms are significant players in the overall balance. This may be attributed to the absence of a tachocline, i. The more turbulent case C is likewise analyzed in Figure 13, and it generally exhibits comparable behavior.

The fluxes for cases A, AB, B, savrat C have been averaged over periods of,and days, respectively.

However, svaart are many fundamental puzzles about the dynamo action that yields the observed fields. This comes about because of both advection and distortion of the cells by the mean zonal flows associated with the differential rotation here at the equator leading to relative angular displacements in longitude of about 70 over one rotation period and fairly rapid evolution and some propagation in their individual downflow patterns Downflow Networks and Variation with Depth The convective structures as delineated by the downflow networks show distinctive changes as the level of turbulence is increased in going from case A to case D.

Regions of convergence and divergence are apparent, as are swirling vortices, which occur most frequently at mid- and high latitudes and generally have a cyclonic sense counterclockwise in the northern hemisphere and clockwise in the southern. The influence of such a layer will await subsequent studies. Examination of Figure 12 at high latitudes does not reveal a savzrt baroclinic contribution, and this is consistent with the bland variation of entropy for case AB Fig.

The strong latitudinal variation of angular velocity observed near the surface, where the rotation is considerably faster at the equator than near the poles, extends through much of the convection zone depth about Mm with relatively little radial dependence. This would be expected since the buoyancy driving has strengthened relative to the dissipative mechanisms as measured by the increasing Rayleigh number R a Table 1.

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

Relative to the Sun, viot motions in the planetary interiors are much more influenced by rotation lower Rossby numbers and diffusion lower Reynolds and magnetic Reynolds numbers and much less influenced by compressibility mild density stratification. Two models, designated as LAM in Miesch et al. We have extended our already well-tested hydrodynamic ASH code see Clune et al.

Helioseismology has revealed that the rotation profiles obtained by inversion of frequency splittings of the p-modes e. In seeking to resolve these two issues, we have explored two paths in parameter space that yield complex and turbulent states of convection.

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 and anisotropic heat transport under the assumption of the separability of scales. Energy bikt balance with radius, averaged over horizontal surfaces and in time.

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

Others believe that the poloidal field is regenerated by the cumulative action of many small-scale cyclonic turbulent motions on the field throughout the convection zone, rather than just close to the surface e. This may come about if baroclinic convective motions produce latitudinal heat flux, leading to a breakdown of the Taylor-Proudman theorem Pedlosky The single-cell behavior there for case AB appears to enable more effective extraction of angular momentum by Reynolds stresses from the high to the low latitudes, thereby yielding a distinctive rotational slowing of the high latitudes.

This strong third cell appears to be of significance in the continuing net poleward transport of angular momentum by the meridional circulations see x 4.

### Index of /Exercices/Magnetostatique

Further, this is accomplished while imposing an upper thermal boundary condition that ensures a uniform emerging heat flux with latitude, as suggested in Elliott et boit.

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 et al. There is evidently some symmetry breaking between the two hemispheres.

In summary, although our solutions attain close to boit thermal wind balance over large portions of the domain, the departures elsewhere are most significant. This may be key in the monotonic decrease of with latitude of case AB extending into the polar regions and provides our first clue for how issue 1 is resolved within this case.

The stronger upper one solid contours representing counterclockwise circulation involves poleward flow that extends from the equator to about 30 latitude near the top of the domain in the northern hemisphere.

The convection in many previous studies of dynamo action in rotating spherical shells is dominated by so-called banana cells: There is further a thin shear boundary layer near the surface in which increases with depth at intermediate and high latitudes. The convection is responsible for transporting outward the solar flux emerging from the deep interior. Er having examined in detail angular momentum flux stream functions savaet shown with radius and latitude consistent with equations 7 9we observed that the Reynolds stress contributions to such transport possessed multicelled structures with radius at high latitudes in all the cases except case AB.

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

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.

We note that our temperature fields show some banding with 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.

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.

The same color scale is used in bcand d.