Effect of density stratification on the thermal convection in a rotating spherical shell

On the basis of the three-dimensional numerical simulation, we study the effect of density stratification on the thermal convection in a rotating spherical shell. Three different density-stratified equilibria, which have different polytropic indices, are adopted as the initial state of the simulation. The density ratio between the bottom and the top of the domain is in the range from 2.0 to 10.7, and the Taylor number is fixed to 10(4). It is found that when the Rayleigh number is slightly above the instability threshold, the convection structure is hardly affected by the difference of stratification, whereas when the Rayleigh number is much larger than the instability threshold, the nonlinear solution in the strongly stratified equilibria bifurcates into the sectorial convection and the quasi-axisymmetric zonal convection. Through the bifurcation from the sectorial solution to the quasi-axisymmetric solution, the sign of the averaged kinetic helicity is changed in each hemisphere (negative to positive in the northern hemisphere). The results suggest that the solar and the stellar convections must be sensitive to the density stratification.