Differential rotation set up by latitude-dependent heat transport

Abstract

Models of differentially rotating compressible deep spherical shells are computed according to the method of Belvedere and Paternò (1977): the heat transport is entirely convective, small-scale motions are parametrized by a thermal diffusivity and a kinematic viscosity, and the limit of slow rotation and large viscosity is considered.

In order to adapt the resulting differential rotation to the observed equatorial acceleration of the Sun, the heat transport must be more effective in the vicinity of the equator. In all models the latitude dependence of the transport coefficient induces meridional circulation in the form of a large cell, with rising material at high latitudes and sinking material near the equator. On top of this cell, one or two thin countercells develop in a minority of cases. Large pole-equator temperature differences and meridonal velocities at the surface are obtained when the Prandtl number is 1. But values of, say, 1/10 are sufficiently small to allow the models to be applied to the Sun. In general an angular velocity increasing with depth is found, and the surfaces of constant angular velocity are inclined towards greater depth and higher latitude.