Convection in rotating non-uniformly stratified spherical fluid shells in dependence on Ekman and Prandtl numbers

We present an investigation of rotating convection in non-uniformly stratified spherical shells in dependence on Prandtl, Ekman and Rayleigh numbers. Attention is focused on the case in which the thickness of both sublayers (stable and unstable) is identical, which was not investigated before. Influence of stratification is more evident at small values of Rayleigh numbers (large values of Ekman numbers), at large Rayleigh numbers is almost negligible. For small Rayleigh numbers in the case of uniform stratification a large-scale columnar convection is developed in the whole volume, in the case of non-uniform stratification it is suppressed to the unstably stratified region but slightly penetrates to the stably stratified one, except the case of large Prandtl numbers when the convection significantly penetrate to the stably stratified region. The spiralling nature of convection is a dominant feature at moderate Prandtl numbers, the strong spiralling is typical at small Prandtl numbers but it disappears at large Prandtl numbers. For large Rayleigh numbers (small values of Ekman numbers) only a small-scale convection is developed. The multilayer convection (“teleconvection”) is not developed in our case of non-uniform stratification because of the significant amount of stable stratification. Our case is a typical extreme case. It is dissimilar to both cases if the stably stratified sublayer is thinner than the unstably stratified one and if the unstably stratified sublayer is thinner than the stably stratified one.