Compressible convection in a rotating spherical shell. V - Induced differential rotation and meridional circulation

Abstract

We describe solutions for the mean differential rotation and meridional circulation in a compressible, rotating, spherical fluid shell which are induced by the linear, anelastic solutions of Papers II and IV for global convection. Our mean solutions strongly depend on the density stratification, the rotation state, the convective velocity distribution, and the amount of viscous diffusion relative to thermal diffusion. In order to obtain an equatorial acceleration which is large in amplitude relative to the meridional circulation, together with a small equator-pole temperature difference, when the density stratification is large as in the solar convection zone, at least one of two conditions must be met: either the effect of rotation must be large compared to the effects of viscous diffusion and buoyancy, or viscous diffusion must be small relative to thermal diffusion. In either case, the angular velocity increases with depth in the upper part of the convection zone by decreases with depth and is nearly constant on cylinders in the lower part when the global convection extends to deep layers. Global convection, differential rotation, and meridional circulation in the deep layers are similar to those found for the incompressible case, while near the top they are quite different.