Abstract
The problem of thermal 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. In our previous paper [Kong, Phys. Rev. Fluids 7, 074803 (2022)], by self-consistently taking into account the centrifugal force, rapidly rotating stably stratified Boussinesq fluid was modeled in oblate spheroidal cavities whose geometric shapes are determined by the theory of figure. A closed-form solution was obtained for gravity and temperature. The stable stratification was demonstrated to be motionless in the corotating frame of reference. Based on this nonspherical model of the conduction state in a rapidly rotating spheroidal cavity, the problem of thermal instability is formulated and discussed by this paper 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 spheroid is systematically explored.
- Received 9 July 2022
- Accepted 12 September 2022
DOI:https://doi.org/10.1103/PhysRevFluids.7.103502
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