The onset of low Prandtl number thermal convection in thin spherical shells

TL;DR

This paper investigates how low Prandtl number influences the onset and pattern of thermal convection in rotating spherical shells, revealing mode transitions and bifurcations relevant to stellar phenomena.

Contribution

It provides new insights into the mode transitions and bifurcations of thermal convection patterns at low Prandtl numbers in rotating spherical shells.

Findings

Transition from spiralling columnar to equatorially-attached modes with decreasing Prandtl number.

Emergence of polar modes at very low Prandtl numbers and high Taylor numbers.

Identification of bifurcation points and transition curves between different convective modes.

Abstract

This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with aspect ratio $\eta=r_i/r_o=0.9$ ($r_i$ and $r_o$ being the inner and outer radius), Prandtl numbers ${\rm Pr} \in[10^{-4},10^{-1}]$, and Taylor numbers ${\rm Ta}\in[10^{4},10^{12}]$. We are particularly interested in the form of the convective cell pattern that develops, and in its time scales, since this may have observational consequences. For a fixed ${\rm Ta}<10^{9}$ and by decreasing ${\rm Pr}$ from 0.1 to $10^{-4}$ a transition between spiralling columnar (SC) and equatorially-attached (EA) modes, and a transition between EA and equatorially antisymmetric or symmetric polar (AP/SP) weakly multicellular modes are found. The latter modes are preferred at very low ${\rm Pr}$. Surprisingly, for ${\rm Ta}>3\times 10^{9}$ the unicellular polar modes become also preferred at moderate ${\rm Pr}\sim10^{-2}$ because two new transition curves between EA and AP/SP and between AP/SP and SC modes are born at a triple-point bifurcation. The dependence on ${\rm Pr}$ and ${\rm Ta}$ of the transitions is studied to estimate the type of modes, and their critical parameters, preferred at different stellar regimes.