On meridian circulation

The meridian circulation velocities in the radiative envelope of a Cowling model star are calculated using a second order perturbation expansion, and it is shown that the circulation breaks up into two regions as obtained by Opik and that the velocity near the surface becomes large as in the case of the first order velocity for non-uniform rotation (Baker & Kippenhahn). This shows that Sweet's first order perturbation method is inadequate for uniform rotation. Also, possible steady state structures with rotations slightly perturbed from uniform rotation are investigated and it is shown that for perturbations of about 3 per cent or less from uniform rotation structures which are in almost steady circulation can be obtained. For larger perturbations of a specified form the circulation breaks up into four regions.