Thermal convection in a differentially heated rotating fluid annulus

A theoretical study of the axi-symmetric fluid motion induced in a rotating annulus by a radial temperature gradient along the lower horizontal surface is made in the limit of small Ekman number, E. Nonlinear convective effects are introduced in the form of an increasing thermal Rossby number, β, and a series of flow regimes occurs corresponding to values of σβ = 0, ∼E2/3, ∼E½ where σ is the Prandtl number of the fluid. In the second of these it is shown that spatial oscillations in the form of convective cells may, or may not, develop in the fluid depending upon the nature of the thermal conditions satisfied at the walls of the annulus. However it is shown that for suitable end-wall boundary conditions the limit in which σβE−½ ≫ 1 is characterised by the formation of a thermal boundary layer in the interior of the fluid, as envisaged by Stern (1975). Stern's interior solution is included in the rigorous asymptotic structure in which the meridional circulation is completed by a strong upwelling of fluid along the hotter of the two end-walls.