Inertial convection in rotating fluid spheres

TL;DR

This paper analyzes the onset of inertial convection in rotating fluid spheres, deriving explicit relations for the Rayleigh number's dependence on azimuthal wavenumber, including new results for insulating boundaries.

Contribution

It extends previous work by providing explicit formulas and new insights into inertial convection with insulating boundary conditions in rotating spheres.

Findings

Derived explicit expressions for Rayleigh number dependence on azimuthal wavenumber.

Obtained new results for nearly thermally insulating boundary conditions.

Extended earlier theoretical analysis of inertial convection in rotating spheres.

Abstract

The onset of convection in the form of inertial waves in a rotating fluid sphere is studied through a perturbation analysis in an extension of earlier work by Zhang (1994). Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived and new results for the case of a nearly thermally insulating boundary are obtained.