Rapidly rotating self-gravitating Boussinesq fluid. IV. Onset of multimodal thermal convection influenced by oblate spheroidal geometry

Convective dynamics in the interiors of rapidly rotating oblate spheroidal planets are generally marked by extremely small Ekman numbers and moderate Prandtl numbers. In the relevant parameter space, at the onset of thermal convection, the flow structure can be represented by the superposition of multiple inertial modes of the same azimuthal wave number. This paper discusses why such thermal convective motions occur and how the degree of flattening of a planet due to rotation would affect the flows. More importantly, the theory discussed in this paper establishes a necessary foundation for future studies of turbulent convection and MHD dynamo actions.