Natural doubly diffusive convection with vibration

Abstract

We present a numerical and analytical study of doubly diffusive convection driven by horizontal thermal and solutal gradients in square and rectangular enclosures with no-slip walls subjected to high-frequency vibration. The two vertical walls of the enclosure are maintained at different but uniform temperatures and concentrations while the horizontal walls are assumed to be impermeable and insulating. The resulting system is described by time-averaged Boussinesq equations. These equations possess a doubly diffusive quasi-equilibrium solution provided the thermal and solutal buoyancy forces are equal and opposite. This solution is linearly stable up to a critical value of the stability parameter independently of the strength and orientation of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength and orientation of the vibration, and the larger amplitude states are computed numerically using a spectral collocation method. For vertical oscillation increasing the vibration amplitude decreases the subcriticality of the solutions and may even reverse it; the opposite occurs with horizontal vibration.