摘要：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. However, the fast rotation of gaseous giant planets and some of Be stars makes them bulge out enough that they can’t be treated as spheres. As a result, investigating the thermal instabilities in oblate spheroids will help researchers better understand the convection processes in these planets and stars or even very flattened systems like accretion disks. In this work, we first derive a nonspherical model of reference state in oblate spheroidal geometry whose shape should be determined by the theory of figure (ToF). A closed-form solution is obtained for gravity and temperature. Based on this nonspherical model of the conduction state, the problem of thermal instability is formulated in the regime of inertial convection, which is marked by an asymptotically small Ekman number and a 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 significant 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.

The related publications:

1. Kong, D. (2022) Rapidly rotating self-gravitating Boussinesq fluid: A nonspherical model of motionless stable stratification, Physical Review Fluids, 7, 074803

2. Li, W., and Kong, D.* (2022) Rapidly rotating self-gravitating Boussinesq fluid. II. Onset of thermal inertial convection in oblate spheroidal cavities, Physical Review Fluids, 7, 103502

3. Li, W., and Kong, D.* (2023) Rapidly rotating self-gravitating Boussinesq fluid. III. A previously unknown zonal oscillation at the onset of rotating convection, Physical Review Fluids (Letter), 8, L011501

简介：Dr. Dali Kong graduated from the Department of Astronomy, Nanjing University, in 2008 and obtained his Ph.D. in Applied Mathematics from the University of Exeter in 2012. He joined Shanghai Astronomical Observatory in 2017 after spending five years of Postdoc fellowship at the Centre for Geophysical and Astrophysical Fluid Dynamics, University of Exeter. Dr. Kong mainly works in planetary fluid dynamics, particularly skilled at analyzing the dynamics of rapidly rotating systems.

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