Numerical study of instabilities of particle-laden fronts in continuously stratified environments

Abstract

Numerical simulations are conducted to study instabilities and the associated convective motion of particle-laden layers settling in continuously stratified environments. We show that when the background density stratification is insignificant relative to the bulk excessive density of the particle-laden layer, the unstable motions of the particle-laden interface are mainly driven by Rayleigh–Taylor instability but become double-diffusive convection when the background stratification is relatively significant. Our results agree with theoretical prediction based on linear stability analysis. However, in the Rayleigh–Taylor instability regime, the motion of particle-laden plumes can be further suppressed by the background density stratification while the plumes reach the height of neutral buoyancy. This leads to the second stage of flow development, in which secondary instability occurs at the plumes' tip in the form of double-diffusive convection. Due to the change in the background density gradient within the plumes' head, the occurrence of secondary instability is accompanied by a shift of the dominant mode, which is particularly significant in cases with a high background Prandtl number (i.e., salinity-induced stratification). The theoretical argument on the mode shift is based on previous linear stability analysis for the two-layer structured background density gradient provided. The ratio between the particles' settling velocity and velocity scaling for the developed local density gradient at the plumes' tip then allows us to distinguish and predict whether the final convective motion is driven mainly by double-diffusive or settling-driven buoyancy-dominant convection.