My research interest is Boussinesq thermal convection in a rotating spherical shell, which is one of the most fundamental framework of the global thermal convection in stellar and planetary interiors. Especially, I am interested in the stability and bifurcation structure of the convection patterns.
I investigated the stability and bifurcation diagram of Boussinesq thermal convection in a moderately rotating spherical shell 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 52^2 to 500^2 and the Rayleigh number is from about to 1500 to 10000. 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 340^2, propataging 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. The decrease of the propagating velocity with the increase of the Rayleigh number can be interpreted as a result of the advection by the strong retrograde mean zonal flows which are generated at the middle of the convection cell near the equatorial plane.
Recently, I am also interested in the torques on inner and outer spheres (cores) induced by the Boussinesq thermal convection in a rotating spherical shell.