Abstract
Stability and bifurcation of Boussinesq thermal convection in a moderately rotating spherical shell are investigated by obtaining finite-amplitude solutions with the Newton method instead of the numerical time integration. The ratio of the inner and outer radii of the shell and the Prandtl number are fixed to 0.4 and 1, respectively, while the Taylor number is varied from 522 to 5002 and the Rayleigh number is from about 1500 to 10 000. In this range of the Taylor number, the stable finite-amplitude solutions, which have four-fold symmetry in the longitudinal (azimuthal) direction, bifurcate supercritically at the critical points and become unstable when the Rayleigh number is increased up to about 1.2 to 2 times the critical values. When the Taylor number is larger than 3402, propagating direction of the solutions changes from prograde to retrograde continuously as the Rayleigh number is increased. The associated transition of the convection structure is also continuous.
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