Convection in a rotating cylindrical annulus: thermal Rossby waves

Abstract

The nonlinear equations describing convection in the form of thermal Rossby waves in a rotating annulus are solved both by an analytical perturbation theory and by a numerical method. It is shown that even in the absence of curvature of the surfaces bounding the fluid annulus in the axial direction a mean flow is generated by Reynolds stresses. The good agreement between analytical expressions and numerical results indicates that the former are valid over a larger domain of the parameter space than may be expected on the basis of the analysis of convection rolls in a non-rotating layer. This is caused in part by the reduced release of potential energy accompanying the reduced convective heat transport owing to the drift of the convection columns. The effect of curvature causes the replacement of the basic mode of convection by a different mode characterized by a double roll structure. The associated zonal mean flow is typically stronger than in the case without curvature.