Journal of Fluid Mechanics

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On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

MARTA NETa1, FERRAN GARCIAa1 and JUAN SÁNCHEZa1

a1 Departament de Física Aplicada, Universitat Politècnica de Catalunya Jordi Girona Salgado s/n. Campus Nord. Mòdul B4, 08034 Barcelona, Spain marta@fa.upc.edu; sanchez@fa.upc.edu

Abstract

Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E < 10−5, the critical Rayleigh number (Rc) fulfils a power-law dependence Rc ~ E−4/3, as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ωc|) and the critical azimuthal wavenumber (mc) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ, E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σxs22730.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small mc can be preferred at the onset of the primary instability.

(Received December 18 2006)

(Revised January 15 2008)

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