Highly supercritical thermal convection in a rotating spherical shell: Centrifugal vs. radial gravity

Abstract

Numerical calculations of fully-developed thermal convection in a rapidly rotating spherical shell are presented. We analyze the three-dimensional structure of convection driven by basal heating at Rayleigh number Ra = 6.67 × 10⁶ and Ekman number E=10⁻⁴ in a shell with the geometry of the Earth's liquid outer core. Calculations using two different body force distributions are compared: radial gravity and centrifugal acceleration. In both cases the flow consists of a chaotic array of small-scale, time-dependent columnar vortices aligned parallel to the rotation axis plus large-scale zonal and meridional circulations. The columnar vortices are driven by thermal plumes localized in the equatorial region. The zonal flow consists mainly of two parts: a cylindrical (geostrophic) part driven by Reynolds stresses derived from the small-scale convection and a thermal wind driven by large-scale temperature gradients. For both body force distributions, convective heat transfer occurs mostly in the equatorial region. The overall structure of the convection, and the resulting zonal flow and longitudinally-averaged helicity are remarkably similar for the two body force distributions outside of the inner core tangent cylinder. In that region of the spherical shell, the component of gravity perpendicular to the rotation axis is the dynamically important component for convection at these Rayleigh and Ekman numbers.