Convective instability in sedimentation: Linear stability analysis

Abstract

[1] Convective sedimentation in a stably stratified saltwater is studied using the linear stability analysis. Convective sedimentation is known to occur due to the double-diffusive mechanism and the settling-driven mechanism. In this study, a semi-empirical closure of sediment diffusivity based on the long-range hydrodynamics effect is adopted. The sediment phase can act as either the slow- or fast-diffusing agent in the double-diffusive system for the given salt diffusivity. Moreover, the settling-driven effect is proportional to the square of the sediment diameter via Stoke settling law. We consider sediment concentration (grain size) in the upper freshwater layer to be in the range of 0.1 to 39.4 g/l (2 to 60 µm), which is on top of a saltwater layer with salinity 35 ppt. Linear stability analysis allows us to identify the dominant mechanism that triggers the instability, the growth rate, and the resulting characteristic finger width. Model results suggest that for fine sediment with grain diameter smaller than 10 µm (settling velocity 0.09 mm/s), double-diffusive mechanism controls the instability and the resulting sediment finger size is of millimeter scale. For the given threshold of growth rate of O(0.01) s−1, the minimum sediment concentration is about 8–15 g/l. For grain size greater than or around 10 µm, the settling-driven mechanism dominates and instabilities occur at sediment concentration as low as O(0.1) g/l with centimeter-scale fingers. Our findings may contribute to a better understanding on the observed rapid sediment removal in the plume of small mountainous rivers.