Effect of fluid properties variations on spatio-temporal instability of convection

Abstract

The classical problem of stability of convection flow in a tall vertical differentially heated rectangular cavity is considered. It is shown that realistic nonlinear fluid properties variations associated with a large cross-cavity temperature gradient lead to significant deviations from the flow scenarios predicted using conventional Boussinesq approximation. It is well known that in the Boussinesq limit of a small temperature gradient the conduction state bifurcates supercritically to a stationary transverse roll pattern associated with the shear of the primary flow, and this instability is of absolute character. Here we show that when the fluid properties vary, a new buoyancy driven oscillatory instability arises, the transition to shear driven instability becomes subcritical, and a range of parameters appears for which the character of instability is convective. Analytical results are obtained by deriving and solving the Ginzburg-Landau-type disturbance amplitude equation and are checked against the results of direct numerical simulation.