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

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Abstract

We present the 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 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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Robinson, F. J., & Chan, K. L. (2001). A large-eddy simulation of turbulent compressible convection: Differential rotation in the solar convection zone. Monthly Notices of the Royal Astronomical Society, 321(4), 723–732. https://doi.org/10.1046/j.1365-8711.2001.04036.x

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