Tidal instability in a rotating and differentially heated ellipsoidal shell

TL;DR

This study numerically investigates how thermal differences influence tidal instability in rotating ellipsoidal shells, revealing that stable temperature fields promote instability and that convection impacts its growth rate, with implications for geophysical flows.

Contribution

It demonstrates the combined effects of thermal and tidal forces on flow stability in ellipsoidal shells, providing new scaling laws and insights relevant to geophysical and astrophysical phenomena.

Findings

Stable temperature fields promote tidal instability.

Tidal instability can grow on convective flows.

Growth rate decreases with increased convection intensity.

Abstract

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows.