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A Large Eddy Simulation of Turbulent Compressible Convection: Differential Rotation in the Solar Convection Zone

Francis J. Robinson·Kwing L. Chan
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Abstract

We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into the deep layers of the convection 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 zonal velocity fluctuations produces a significant Reynolds stress in that region. This constitutes a net transport of angular momentum inwards, which causes a slight modification of the overall structure of the differential rotation near the top. In essence, the {\it thermodynamics controls the dynamics through the Taylor-Proudman momentum balance}. The Reynolds stresses only become significant in the surface layers, where they generate a weak meridional circulation and an angular velocity `bump'.

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Francis J. Robinson, Kwing L. Chan. 2000-11-21. A Large Eddy Simulation of Turbulent Compressible Convection: Differential Rotation in the Solar Convection Zone. https://doi.org/10.1046/j.1365-8711.2001.04036.x

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