The Effect of a Salinity Gradient on the Instability of Natural Convection in a Vertical Fluid Layer

The effect of a salinity gradient on the instability of natural convection in a vertical fluid layer between two parallel plates is investigated theoretically. Temperatures of the two plates are different by 2T₀ and both a stable temperature gradient, β>0, and an unstable salinity gradient, β_s>0, are present in the vertical direction. The stability is investigated for various values of β and β_s in the case of the Prandtl number P_r{=}7 and the Schmidt number S_c{=}700, which corresponds to weak salt water. It is found that the stationary mode dominates the onset of instability if both β and β_s are moderate, otherwise the travelling mode governs it.