Rapidly rotating self-gravitating Boussinesq fluid. II. Onset of thermal inertial convection in oblate spheroidal cavities

Abstract

For decades researchers have been studying the problem of thermal instabilities in rotating spheres or spherical shells. A key assumption is that the geometrical flattening due to centrifugal force can be neglected, which seems to be a good approximation for many planets and stars. However, this has never been tested. In this paper, the linear stability onset problem at low Prandtl number is considered in oblate spheroids, whose shapes are consistent with figure theory, and it is compared with the previously known spherical system solutions.