• PHYSICAL PROBLEM: The Sun's convective zone is not rotating like a rigid body; why? Where does the differential rotation come from?

 
• OBSERVATIONS: Helioseismic data (SOHO, GONG) measure the so-called 5-minutes acoustic oscillations . By probing the internal structure of the Sun these oscillations allow us to determine for example the sound speed and the angular velocity as a function of depth and latitude.

 
• EQUATIONS: Navier-Stockes equation in a rotating frame with heat diffusion within the anelastic approximation (i.e. which filter out the sound waves) in a three-dimensional spherical geometry

 
• NUMERICAL EXPERIMENT: Evolution of a stratified, convecting fluid, under the influence of rotation, no-stress, impenetrable boundary conditions, with constant entropy gradient.

 
• CONCLUSION: The large-scale meridional circulation and the small-scale turbulent convection play a dominant role in the redistribution of the angular momentum and in the onset of a differential rotation without cylindrical symmetry.

 
• REFERENCE: Mean Flow in Convective Rotating Turbulent Shells, A.S. Brun & J. Toomre, contribution meeting Soho10, octobre 2000.

FILM 1 : (mpeg, visible with xanim, 0.9 Mb) radial velocities close to the solar surface (somewhat below: 0.95 R_s) during a solar rotation

FILM2 : (mpeg, visible with xanim, 0.2 Mb) volumes revealing downward radial velocities in the interior of the convective zone (between 0.73 and 0.95 R_s)
 
 

spherical coordinates (r, theta, phi); Resolution: 192 x 512 x 1024

Boundary Conditions (both top and bottom): stress-free, impenetrable, constant heat flux

Sun's rotation period: 28 Days

Main Initial Parametres:

Rayleigh = 6.5 10^5, Taylor = 6.5 10^6, Prandtl (nu/kappa) = 0.25, Convective Rossby number = sqrt(Ra/TaPr) = 0.63

Density Contrast between top and bottom: 25

Kinematic viscosity nu and thermal diffusivity kappa vary as 1/density

Temporal averages in the middle of the domain:
Reynolds: Re_max ~1700, Re_rms~190; Rossby Ro_rms~0.07 (i.e omega_rms/2Omega)

For 100 iterations the duration of the run is about 0.3 Day.
Hence for these films more than 10000 iterations have been necessary.
During 50 hours with 64 processors, 1000 iterations have been made. Hence, 30000 node-hours for the film.
About 80000 hours. finally for all.