A large-eddy simulation of turbulent compressible convection: differentialrotation in the solar convection zone

We present the results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shel l. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the ent ire depth. The second simulation has isorotation contours about mid-way bet ween cylinders and cones, and a weak meridional circulation, concentrated i n the uppermost part of the shell. We show that the solar differential rotation is directly related to a latit udinal entropy gradient, which pervades into the deep layers of the convect ion zone. We also offer an explanation of the angular velocity shear found at low latitudes near the top. A non-zero correlation between radial and zo nal velocity fluctuations produces a significant Reynolds stress in that re gion. This constitutes a net transport of angular momentum inwards, which c auses a slight modification of the overall structure of the differential ro tation near the top. In essence, the thermodynamics controls the dynamics t hrough the Taylor-Proudman momentum balance. The Reynolds stresses only bec ome significant in the surface layers, where they generate a weak meridiona l circulation and an angular velocity 'bump'.