Theory of Axisymmetric Thermal Convection in a Rotating Fluid Annulus

A simplified theoretical model is presented of axisymmetric thermal convection in an annulus of liquid of kinematical viscosity ν, thermal diffusivity κ, and thermal coefficient of cubical expansion α, which rotates at Ω rad/sec about a vertical axis and is subject to a horizontal temperature contrast of |ΔT| C°. Ω is such that although Coriolis forces are in (geostrophic) balance with horizontal pressure gradients throughout most (though not all) parts of the fluid, centripetal acceleration is everywhere much less than that due to gravity, g. When an appropriate Péclét number, proportional to X=gα|ΔT|ν12/8κΩ32, is very small, heat conduction dominates the temperature field and the governing equations can be linearized. Otherwise the governing equations are essentially nonlinear, and when X is very large the temperature field is dominated by heat advection. The expressions obtained for the mean thermal structure and heat transfer agree satisfactorily with an analytical treatment of the small X case and with laboratory and numerical studies of the large X case. The expression obtained for the Brunt-Väisälä frequency, when combined with baroclinic instability theory, predicts that the axisymmetric flow should give rise to a definite type of nonaxisymmetric flow under conditions that agree remarkably well with laboratory studies.