Two-dimensional stochastic motions and the problem of differential rotation

Abstract

This paper deals with the spatial dependence of the angular velocity in a rotating turbulent fluid sphere. The original turbulence unaffected by the global rotation is assumed to be two-dimensional where the stochastic force field producing the turbulence does not possess a radial component. By using results of earlier papers we proceed to the treatment of a rotational rate, Ω, no longer small compared to Ω _c (frequency of turbulent mode). It is shown that for Ω≪Ω _c the angular velocity increases with increasing radius but no latitudinal dependence exists. Contrary to this, for 2Ω∼Ω _c an equatorial acceleration is possible and related to negativity of the two-dimensional eddy viscosity. Furthermore, the outer layers rotate faster than the inner ones. These findings coincide with Gilman's numerical results. Ward's observations, as well as the characteristic scales of supergranulation and giant cells, suggest the presence of negative two-dimensional eddy viscosity on the Sun.