Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

TL;DR

This study investigates nonlinear convection in a rapidly rotating sphere with liquid metal properties, revealing two distinct convection branches, subcritical behavior at low Ekman numbers, and the influence of Prandtl number on convection dynamics.

Contribution

It introduces a quasi-geostrophic numerical model to identify and analyze two convection branches, including a novel subcritical strong branch at low Ekman numbers, in liquid metal-like conditions.

Findings

Two convection branches identified: weak supercritical and strong subcritical.

Subcritical convection occurs at Ekman numbers around 10^{-8}.

Hysteresis and nonlinear oscillations are observed near convection onset.

Abstract

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.