Onset of low Prandtl number thermal convection in thin spherical shells

This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with an aspect ratio η = ri/ro = 0.9 (ri and ro being the inner and outer radius), Prandtl numbers Pr ∈ [10−4,10−1], and Taylor numbers Ta ∈ [104,1012]. 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 Ta < 109 and by decreasing Pr from 0.1 to 10−4, a transition between spiraling 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 Pr. Surprisingly, for Ta > 3 × 109, the unicellular polar modes become also preferred at moderate Pr ∼ 10−2 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 Pr and Ta of the transitions is studied to estimate the types of modes, and their critical parameters, preferred at different stellar regimes.