MERIDIONAL CIRCULATION IN ROTATING STARS. XI. SINGLE-CELL PATTERN VERSUS DOUBLE-CELL PATTERN

摘要

An analytical-numerical study is made of the thermally driven meridional currents and concomitant differential rotation in the radiative envelope of a nonmagnetic, early-type star. Since we cannot possibly encompass all the timescales and space scales of motion in a star, we make use of steady state models to represent these large-scale motions, while applying parametric expressions to describe the effects of all smaller scales. Assuming that the departures from spherical symmetry are not too large, we expand the solutions about hydrostatic equilibrium in powers of the rotational parameter ε, which is the ratio of the centrifugal force to gravity at the equator. Thence, by making allowance for turbulent friction acting on the mean flow (i.e., the differential rotation and the meridional currents), we obtain second-order solutions in ε that satisfy all the basic equations and all the boundary conditions. As a matter of fact, there exist thin thermoviscous boundary layers, so that the currents do not become infinite near the boundaries, the meridional velocities remaining uniformly small throughout the radiative envelope. Simultaneously, the frictional force acting on the differential rotation can be made to balance the transport of angular momentum by the large-scale meridional flow. The proposed solution is a diffusive one, in the sense that the effects of vertical dissipation are assumed to be larger than those caused by the thermally driven currents.