Flow Structure of Thermal Convection in a Rotating Spherical Shell

"A convoluted pattern of streamlines in a steady state of thermal convection of a Boussinesq fluid between two concentric spheres rotating with a common angular velocity is investigated numerically at Rayleigh number 3200, Taylor number 8000, Prandtl number 1, and the radius ratio 0.5 of the two spheres. Five pairs of Taylor-Proudman vortex columns with opposite rotation are generated, which arrange alternatively parallel to the axis of rotation across the middle in the equatorial plane of the spherical shell. These vortex columns retrograde at a constant angular velocity. The flow field is steady in a frame rotating with this angular velocity. The velocity filed is symmetric with respect to the equatorial plane. Two kinds of nontrivial closed streamlines which turns once around the rotating axis of the spheres and seven different kinds of non-trivial stagnation points of velocity are found in the steady flow frame. The entangled topological structure of the velocity field is resolved by visualization of closed streamlines and streamlines emanating from stagnation points.