Linear stability analysis of the convective flow in a spherical gap with rotating inner surface

Abstract

We consider the flow in the spherical gap with the radii ratio η=R1/R2=0.5, which is caused by the axial buoyancy force and rotation of the inner surface. The inner surface is warmer than the outer surface (T1 > T2). The basic flow is axisymmetric but has a completely different structure in the northern and southern hemispheres. While buoyancy and Ekman pumping forces compete with each other in the upper hemisphere, they have the same direction in the lower hemisphere. For the fluid, a linear stability analysis with the Prandtl number Pr=0.015 was performed. We calculate the critical Grashof number as a function of the Reynolds number Grc(Re). We have also found that the basic flow becomes unstable with respect to the non-axisymmetric perturbations. The bifurcation sets in as oscillating. We also present some examples of the fully developed three-dimensional flow.