Onset of thermohaline convection in a rectangular porous cavity in the presence of vertical vibration

Abstract

Double diffusive convection in a two-dimensional rectangular cavity with imposed vertical differences in temperature and concentration is considered in the presence of high-frequency vertical vibrations. Linear stability analysis permits the domains of oscillatory and stationary convection thresholds to be delimited. Depending on the governing parameters, vibrations are found to delay or speed up the onset of convection. The effect of vibration on the flow structure near the bifurcation is also analyzed, showing different possible behaviors. The stationary bifurcation is then studied by means of a weakly nonlinear analysis. In agreement with the symmetries present in the problem, this bifurcation is found to be pitchfork. The parametric ranges where it can be subcritical or supercritical are precisely delimited. Finally, direct numerical simulations have been performed to confirm and illustrate these findings.