Numerical simulations of thermal convection in a rotating spherical fluid shell at high Taylor and Rayleigh numbers

Abstract

In this study, we carry out numerical simulations of thermal convection in a rapidly rotating spherical fluid shell at high Taylor number Ta and Rayleigh number R with a nonlinear, three-dimensional, time-dependent, spectral-transform code. The parameters used in the simulations are chosen to be in a range which allows us to study two different types of convection, i.e., single column and multi-layered types, and the transition between them. Numerical solutions feature highly time-dependent north–south open columnar convective cells. The cells occur irregularly in longitude, are quasi-layered in cylindrical radius, and maintain alternating bands of mean zonal flow. The complex convective structure and the banded mean zonal flow are results of the high Taylor and Rayleigh numbers. The transition between the two types of convection appears to occur gradually with increasing Rayleigh and Taylor numbers. At a Taylor number of 107 the differential rotation pattern consists of an inner cylindrical region of subrotation and an outer cylindrical shell of superrotation manifest at the outer boundary as an equatorial superrotation and a high latitude subrotation. The differential rotation pattern is similar at Ta=108 and low Rayleigh number. Cylindrical shells of alternately directed mean zonal flow begin to develop at Ta=108 and R=50Rc and at Ta=109 and R=25Rc. This pattern is seen on the outer surface as a latitudinally-banded zonal flow consisting of an equatorial superrotation, a middle and high latitude subrotation, and a polar superrotation. At Ta=109 and R=50Rc the differential rotation appears at the surface as a broad eastward flow in the equatorial region with alternating bands of westward and eastward flow at high latitudes.