The onset of thermal inertial convection in a rapidly rotating oblate spheroidal liquid core

Abstract

<p>Motivated by its applications to the core dynamics in the Earth and other Planets, the problem of convective instability in rapidly rotating, self-gravitating fluid bodies has been widely modeled in spheres or spherical shells, which implicitly neglects the flattening effect due to the centrifugal force. By self-consistently taking into account the centrifugal force, rapidly rotating stably stratified Boussinesq fluid is firstly modeled in oblate spheroidal cavities whose geometric shapes are self-consistently determined by the theory of figure. A closed-form solution is obtained for gravity and temperature. Based on this nonspherical model of the conduction state in a rapidly rotating spheroidal cavity, the problem of thermal instability is formulated and analytically discussed in the regime of inertial convection, which is marked by asymptotically small Ekman number and sufficiently small Prandtl number. The critical properties of inertial modes are explicitly derived. The dependence of the onset of thermal inertial convection on the oblateness of the spheroid is systematically explored. A remarkable discovery is that the globally most unstable mode could switch from a non-axisymmetric quasi-geostrophic wave to an equatorially symmetric zonal oscillation when the rotational flattening effect gets very strong. This was the only form of global convection not found so far.</p>