The onset of low Prandtl number thermal convection in thin spherical shells
| Autor: | Garcia, F., Chambers, F. R. N., Watts, A. L. |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Accepted for publication in Physical Review Fluids. Contains 17 pages, 8 figures and 3 tables. Added brief erratum correcting values used for estimates of neutron star ocean viscosity |
| Databáze: | arXiv |
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