Centrifugally driven thermal convection in a rotating cylinder

Abstract

Thermally induced convection in a rotating cylinder of fluid heated from above and strongly influenced by centrifugal accelerations is treated using boundary-layer methods. As in the theory of homogeneous rotating fluids, the horizontal Ekman layers control the inviscid axial flow. The solution also largely depends upon the thermal conditions assumed at the side wall, and if these be insulated, consideration of the side-wall boundary layers is necessary for complete specification of the problem. For perfectly conducting side walls, the side layers do not influence the zeroth-order flow, but contribute a second-order correction, which would be absent if the lateral boundaries were ignored. The critical parameters governing the solutions in both cases are found to be γ and the group σβε^−½, where γ is the aspect ratio, σ the Prandtl number, ε the Ekman number, and β the thermal Rossby number for the flow. Boundary-layer solutions are given for a wide range of parameters, and gravity is seen to have at most only a local effect on the flow near the side walls.