Onset of thermosolutal convective regimes in a rectangular porous cavity

The onset of thermosolutal convection in a rectangular cell filled with a porous medium saturated by a binary fluid is studied. The vertical walls are maintained at different, but uniform, temperatures and concentrations. The horizontal walls are impermeable and adiabatic. When the ratio of resulting solutal and thermal buoyancy forces is equal to -1, we obtain an equilibrium solution corresponding to a purely diffusive regime. We demonstrate that this regime is linearly stable up to a critical thermal Rayleigh number, Ra-c1, depending on the aspect ratio of the cell and the Lewis number. These analytical results are in good agreement with numerical direct simulations which allow us to describe the double-diffusive convective regimes taking place when the equilibrium regime loses its stability.