A new asymptotic method for the analysis of convection in a rapidly rotating sphere

Abstract

Thermal convection in rapidly rotating, self-gravitating Boussinesq fluid spheres is characterized by three parameters: the Rayleigh number .In addition to the linear problem of thermal convection in rapidly rotating spheres, the corresponding weakly nonlinear problem is also solved to obtain an analytical expression for the convection-driven differential rotation generated by the nonlinear interaction of quasi-geostrophic-inertial-wave modes through the Reynolds stresses. The new method not only reveals the underlying nature of thermal convection in rapidly rotating spheres but also unites the two previously disjointed subjects in rotating fluids: the inertial-wave problem and the convective instability problem.