Varying the spherical shell geometry in rotating thermal convection

Abstract

The effect of spherical shell geometry on rapidly-rotating thermal convection is studied in a suite of high resolution three-dimensional numerical simulations. The geometry is characterized by the radius ratio, χ = ri/ro , where ri is the inner shell radius, and ro is the outer shell radius. In this study, χ is varied over the broad range 0.10 to 0.92 in calculations of Boussinesq rotating convection subject to isothermal, rigid boundary conditions. Simulations are performed at Prandtl number Pr = 1 and for Ekman numbers E = 10−3, 3 × 10−4 and 10−4. Near the onset of convection, the flow takes the form of rolls aligned parallel to the rotation axis and situated adjacent to the inner shell equator. The dimensionless azimuthal wavelength, λ c , of the rolls is found to be independent of the shell geometry, only varying with the Ekman number. The critical wave number, mc , of the columnar rolls increases in direct proportion to the inner boundary circumference. For our simulations the critical Rayleigh number Rac at which convection first occurs varies in proportion to E −1.16; a result that is consistent with previous work on rotating convection. Furthermore, we find that Rac is a complex function of χ. We obtain the relation , which adequately fits all our results. In supercritical convection calculations the flows form quasi-geostrophic sheet-like structures that are elongated in the radial direction, stretching from the inner boundary toward the outer boundary.