D.J. Ivers
School of Mathematics and Statistics , University of Sydney, Sydney, Australia.
The thermal instability of a self-gravitating Boussinesq fluid in a rotating rigid oblate spheroid is driven by uniformly-distributed heat sources. The rotation is co-axial with the axis of symmetry. The linear instability of the fluid is investigated numerically. The spherical toroidal-poloidal representation is generalised to spheroids. The momentum equation differs from the spherical case by an anisotropic viscous diffusion and a pressure gradient. The thermal diffusion in the heat equation is also anisotropic. The equations are discretised using spherical harmonic expansions of the toroidal-poloidal potentials and the temperature in angle and finite differences in scaled radius. The linearised instability problem then reduces to a generalised eigen- and critical-value problem. Preliminary work on extension of the method to non-linear convection, and its application to the effect of precession on the Earth's core and topographical core-mantle coupling will also be given.