Rapidly rotating plane layer convection with zonal flow

TL;DR

This paper investigates the onset of convection in rapidly rotating planetary interior models with thermal winds, revealing a transition between convective and baroclinic instabilities influenced by thermal wind effects, with implications for Earth's dynamo.

Contribution

It provides a detailed analysis of the transition between convective and baroclinic instabilities in rotating layers with thermal winds, including asymptotic solutions and relevance to planetary dynamos.

Findings

Thermal wind destabilizes convective modes.

Long wavelength modes are the first to become unstable.

Baroclinic instability can occur with stable vertical temperature gradients.

Abstract

The onset of convection in a rapidly rotating layer in which a thermal wind is present is studied. Diffusive effects are included. The main motivation is from convection in planetary interiors, where thermal winds are expected due to temperature variations on the core-mantle boundary. The system admits both convective instability and baroclinic instability. We find a smooth transition between the two types of modes, and investigate where the transition region between the two types of instability occurs in parameter space. The thermal wind helps to destabilise the convective modes. Baroclinic instability can occur when the applied vertical temperature gradient is stable, and the critical Rayleigh number is then negative. Long wavelength modes are the first to become unstable. Asymptotic analysis is possible for the transition region and also for long wavelength instabilities, and the results agree well with our numerical solutions. We also investigate how the instabilities in this system relate to the classical baroclinic instability in the Eady problem. We conclude by noting that baroclinic instabilities in the Earth's core arising from heterogeneity in the lower mantle could possibly drive a dynamo even if the Earth's core were stably stratified and so not convecting.