Equilibrium problems in a rotating convection zone

This paper is a continuation of the author's work on stellar convection (Vandakurov, 1975a; hereafter referred to as Paper I). The approximate equations for convective perturbations in Paper I are somewhat corrected and generalized to include both nonlinear terms and possible variations in molecular weight. A crude estimate of the nonlinear terms is given by means of an expansion of the solution in powers of the perturbation amplitude. We assume that only the most rapidly growing unstable modes are of significance and that the initial kinetic energy of each independent mode is the same. An expansion in powers of the angular velocity is also performed. (This means that some upper stellar layers with small, but not very small, superadiabaticity are considered.) It is shown that an azimuth-averaged azimuthal force is created by the unstable perturbations. In particular, it is most likely that in the upper part of any stellar convection envelope the rigid rotation is nonequilibrious. A simple formula for the above azimuthal force is derived in the case of a latitudedependent angular velocity and a small viscosity of the medium. If the perturbed characteristic scaleheight is sufficiently small, the azimuthal force created by the most unstable modes is equivalent to a viscous force, but with a negative viscosity coefficient. In the approximation under consideration, the heat flux is spherically symmetric.