Onset of inertial magnetoconvection in rotating fluid spheres

TL;DR

This paper analyzes the initiation of magneto-inertial convection in a rotating fluid sphere with axial current, deriving explicit relations for critical parameters under different thermal boundary conditions.

Contribution

It provides new explicit formulas for the Rayleigh number dependence on azimuthal wavenumber in magneto-inertial convection within rotating spheres.

Findings

Derived explicit expressions for Rayleigh number versus azimuthal wavenumber.

Analyzed effects of thermal boundary conditions on convection onset.

Identified conditions for magneto-inertial wave initiation.

Abstract

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied through a perturbation analysis. Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained.