Stability of stratified natural convection in a tall vertical annular cavity

Abstract

The stability of buoyancy-driven convection between vertical concentric cylinders is examined under vertical thermal stratification conditions, with a uniform temperature gap between the cylinders. Analytical solutions are derived for the parallel base flow. Critical Rayleigh numbers are determined from these solutions at various Prandtl numbers, stratification levels, and inner to outer radius ratios. Nonaxisymmetric critical disturbances can be found for low radius ratios and small Prandtl numbers, but are otherwise symmetric and usually occur in the form of travelling waves opposite to gravity, except at large Prandtl numbers and for strong stratification where the direction of propagation is reversed. The effect of curvature is to favor the onset of instability at any stratification level, for moderate and large Prandtl numbers. For small Prandtl numbers, curvature has a stabilizing effect at low stratification levels and is most influential at moderate levels. Computation of the Landau coefficient reveals that the bifurcations are at times subcritical, depending on the parameter values.