Double-diffusive sedimentation

Abstract

Double-diffusive sedimentation Peter Burns and Eckart Meiburg Department of Mechanical Engineering UC Santa Barbara Santa Barbara, CA 93106 Email: meiburg@engineering.ucsb.edu Abstract When a layer of particle-laden fresh water is placed above clear, saline water, both double- diffusive and Rayleigh–Taylor instabilities may arise. We explore the competition between these instabilities by means of two- and three-dimensional direct numerical simulations (DNS). The initial instability growth in the DNS is seen to be consistent with the dominant modes predicted by the linear stability analysis. The subsequent vigorous growth of individual fingers gives rise to a secondary instability, and eventually to the formation of intense plumes that become detached from the interfacial region, cf. figure 1. The simulations show that the presence of particles with a Stokes settling velocity modifies the traditional double-diffusive fingering by creating an unstable ‘nose region’ in the horizontally averaged profiles, located between the upward-moving salinity and the downward-moving sediment interface. The effective thickness l s (l c ) of the salinity (sediment) interface grows diffusively, as does the height H of the nose region. The ratio H/l s initially grows and then plateaus, at a value that is determined by the balance between the flux of sediment into the rose region from above, the double-diffusive/Rayleigh–Taylor flux out of the nose region below, and the rate of sediment accumulation within the nose region. For small values Figure 1: Contours of the sediment field showing upwards propagating fingers.