Settling-driven instability in two-component stably stratified Hele-Shaw flows

Abstract

We investigate the onset of instability in a stably stratified two-component fluid in a vertical Hele-Shaw cell when the unstably stratified scalar has a settling velocity. This linear stability problem is analysed on the basis of Darcy’s law, for constant-gradient base states. The settling velocity is found to trigger a novel instability mode characterized by pairs of inclined waves. For unequal diffusivities, this new settling-driven mode competes with the traditional double-diffusive mode. Below a critical value of the settling velocity, the double-diffusive elevator mode dominates, while, above this threshold, the inclined waves associated with the settling-driven instability exhibit faster growth. The analysis yields neutral stability curves and allows for the discussion of various asymptotic limits.