Solutions are described for the mean differential rotation and meridional circulation in a compressible, rotating, spherical fluid shell which are induced by linear, anelastic solutions for global convection. The mean solutions strongly depend on the density stratification, the rotation rate, the convective velocity distribution, and the amount of viscous diffusion relative to thermal diffusion. It is noted that at least one of two conditions must be met in order to obtain an equatorial acceleration that is large in amplitude relative to the meridional circulation (together with a small equator-pole temperature difference) when the density stratification is as large as in the solar convection zone. Either the effect of rotation must be large compared with 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 but decreases with depth and is nearly constant on cylinders in the lower part when the global convection reaches deep layers.
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Glatzmaier et al. (1982) studied this question.