Torques on the Inner and Outer Spheres Induced by the Boussinesq Thermal Convection in a Rotating Spherical Shell

Abstract

We investigate the directions and amplitudes of torques on the inner and outer spheres induced by the stable finite-amplitude traveling wave solutions which bifurcate supercritically at the critical points and have four-fold symmetry in the azimuthal direction under the impermeable, no-slip and fixed-temperature boundary conditions. The ratio ratio of inner and outer radii η=0.4 and the Prandtl number P =1, while the Taylor number is varied from 52 2 to 500 2 and the Rayleigh number is from about R c to 1.2-2 R c , where R c is the critical Rayleigh number. It is shown that the direction of the torque on the inner sphere is prograde at small Taylor numbers, while it becomes retrograde at large Taylor numbers. Weakly nonlinear analyses show that the nonlinear term in the energy equation is most effective to generate the global distribution of mean zonal flows, however, the azimuthal component of the nonlinear term in the Navier–Stokes equation becomes most important for generation of the torque on the inne...