Multiple Solutions for a Flow between Two Concentric Spheres with Different Temperatures and Their Stability

Abstract

Finite amplitude steady solutions for convections between two concentric spheres under the effects of differential rotation and temperature difference between the spheres are obtained and their linear stability is investigated numerically. Under the assumption of axisymmetry about the axis of rotation, the solutions are classified into the symmetric solution and the asymmetric solution with respect to the equator. It is found that the symmetric solution consists of the upward solution and the downward solution which have different flow profiles, rates of heat transfer between two spheres. A perfect pitchfork bifurcation is observed for the asymmetric solution, whereas an imperfect pitchfork bifurcation is observed for the symmetric solution, as the rate of the differential rotation is increased.