We investigate the stability and bifurcation of Boussinesq thermal convection in a moderately rotating spherical shell, with the inner sphere free to rotate as a solid body due to the viscous torque of the fluid. The ratio of the inner and outer radii of the spheres and the Prandtl number are fixed to 0.4 and 1, respectively. The Taylor number is varied from 522 to 5002 and the Rayleigh number from 1500 to 10 000. In this parameter range, the finite-amplitude traveling wave solutions, which have four-fold symmetry in the azimuthal direction, bifurcate supercritically at the critical points. The inner sphere rotates in the prograde direction due to the viscous torque of the fluid when the rotation rate is small while it rotates in the retrograde direction when the rotation rate is large. However, the stable region of these traveling wave solutions is quantitatively similar to that in the co-rotating system where the inner and outer spheres rotate with the same angular velocity. The structures of convective motions of these solutions such as the radial component of velocity are quantitatively similar to those in the co-rotating system, but the structure of mean zonal flows is effectively changed by the inner sphere rotation.
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