Differentially heated flow from a rotating sphere

Abstract

We present results on the flow of a thin fluid layer over a rotating sphere having a surface temperature that varies with latitude. The fluid is taken to be viscous, incompressible and Newtonian while the flow is assumed to possess both azimuthal and equatorial symmetry. The governing Navier-Stokes and energy equations are formulated in terms of a stream function and vorticity. An approximate analytical solution for the steady-state flow has been derived and is compared with numerical solutions to the steady and unsteady governing equations. For small Rayleigh numbers these solutions are found to be in close agreement. However, as the Rayleigh number is increased noticeable differences occur. A numerical solution procedure is presented along with a procedure for obtaining an approximate analytical solution.