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

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 $\mathrm{Pr}\in [10^{-4},10^{-1}]$, and Taylor numbers $\mathrm{Ta}\in [10^4,10^{12}]$. 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 $\mathrm{Ta}<10^9$ and by decreasing $\mathrm{Pr}$ 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 $\mathrm{Pr}$. Surprisingly, for $\mathrm{Ta}>3\times 10^9$ the unicellular polar modes become also preferred at moderate $\mathrm{Pr}\sim 10^{-2}$ 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 $\mathrm{Pr}$ and $\mathrm{Ta}$ of the transitions is studied to estimate the type of modes, and their critical parameters, preferred at different stellar regimes.

arXiv commentAccepted 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

References in corpus (19)

• Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation
• Predicting solar cycle 24 with a solar dynamo model
• Thermonuclear burst oscillations
• Propagation of thermonuclear flames on rapidly rotating neutron stars: extreme weather during type I X-ray bursts
• Seismic Sounding of Convection in the Sun
• A common origin of magnetism from planets to white dwarfs
• Reconciling solar and stellar magnetic cycles with nonlinear dynamo simulations
• R-Modes on Rapidly Rotating, Relativistic Stars: I. Do Type-I Bursts Excite Modes in the Neutron-Star Ocean?
• Hydrodynamic simulations of He-shell flash convection
• The core helium flash revisited: II. Two and three-dimensional hydrodynamic simulations
• Flame Propagation on the Surfaces of Rapidly Rotating Neutron Stars during Type I X-ray Bursts
• Thermonuclear Bursts with Short Recurrence Times from Neutron Stars Explained by Opacity-Driven Convection
• Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a Pure Helium Accretor
• Scaling laws for convection and jet speeds in the giant planets
• Inertial convection in rotating fluid spheres
• Rotational effects in thermonuclear Type I Bursts: equatorial crossing and directionality of flame spreading
• Multidimensional Modeling of Type I X-ray Bursts. II. Two-Dimensional Convection in a Mixed H/He Accretor
• The Breakdown of the Anelastic Approximation in Rotating Compressible Convection: Implications for Astrophysical Systems
• Fast and slow magnetic deflagration fronts in Type I X-ray bursts