On the Dynamics of the Solar Convection Zone

Abstract

We derive expressions for the turbulent viscosity and turbulent conductivity applicable to convection zones of rotating stars. We assume that the dimensions of the convective cells are known and derive a simple distribution function for the turbulent convective velocities under the influence of rotation. From this distribution function (which includes, in particular, the stabilizing effect of rotation on convection) we calculate in the mixing-length approximation: i) the turbulent Reynolds stresstensor and ii) the expression for the heat flux in terms of the superadiabatic gradient. The contributions of the turbulent convective motions to the mean momentum and energy equation are treated consistently, and assumptions about the turbulent viscosity and heat transport are replaced by assumptions about the turbulent flow itself. The free parameters in our formalism are the relative cell sizes and their dependence on depth and latitude.