# Subcritical thermal convection of liquid metals in a rapidly rotating sphere

## TL;DR

This study investigates nonlinear thermal convection in rapidly rotating liquid metal spheres, revealing subcritical bifurcation, hysteresis, and the dominance of advection over wave-like convection near planetary core conditions.

## Contribution

It demonstrates that in rapidly rotating planetary cores, convection can persist below linear onset through subcritical bifurcation and hysteresis, highlighting the role of Reynolds stress.

## Key findings

- Convection onsets as thermal Rossby waves near critical Rayleigh number.
- At higher Ra, convection transitions to advection-dominated states.
- Strong branch convection persists below linear onset, indicating subcriticality.

## Abstract

Planetary cores consist of liquid metals (low Prandtl number $Pr$) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number $Ek$) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the P\'eclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.