Convective instability in sedimentation: 3-D numerical study

Abstract

To provide a probable explanation on the field observed rapid sedimentation process near river mouths, we investigate the convective sedimentation in stably stratified saltwater using 3-D numerical simulations. Guided by the linear stability analysis, this study focuses on the nonlinear interactions of several mechanisms, which lead to various sediment finger patterns, and the effective settling velocity for sediment ranging from clay (single-particle settling velocity V 0 5 0.0036 and 0.0144 mm/s, or particle diameter d 5 2 and 4 lm) to silt (V 0 5 0.36 mm/s, or d 5 20 lm). For very fine sediment with V 0 5 0.0036 mm/s, the convective instability is dominated by double diffusion, characterized by millimeter-scale fingers. Gravitational settling slightly increases the growth rate; however, it has notable effect on the downward development of vertical mixing shortly after the sediment interface migrates below the salt interface. For sediment with V 0 5 0.0144 mm/s, Rayleigh-Taylor instabilities become dominant before double-diffusive modes grow sufficiently large. Centimeter-scale and highly asymmetric sediment fingers are obtained due to nonlinear interactions between different modes. For sediment with V 0 5 0.36 mm/s, Rayleigh-Taylor mechanism dominates and the resulting centimeter-scale sediment fingers show a plume-like structure. The flow pattern is similar to that without ambient salt stratification. Rapid sedimentation with effective settling velocity on the order of 1 cm/s is likely driven by convective sedimentation for sediment with V 0 greater than 0.1 mm/s at concentration greater than 10-20 g/L.

Sedimentation from flocculated suspensions in the presence of settling‐driven gravitational interface instabilities

“…The initial studies of Burns and Meiburg [2012] and Yu et al [2013] both suggested that when the Stokes diameter of the sediment in the freshwater layer is greater than approximately 10 lm, it is likely that settling-driven convection will dominate at isothermal conditions under salt induced stratification. The 3-D simulations of Yu et al [2014] for three different particles sizes (2, 4, and 20 lm) under a range of concentrations (4-32 g/L) confirmed and further teased out the conditions that will lead to different instability modes by showing that for unflocculated clay (d5 2-4 lm) salt stratification at isothermal conditions should lead to double-diffusive dominated instabilities. However, as sediment size shifts up into the silt range (d 5 20 lm), the dominant mode shifts toward settling driven leaking.…”

“…This produces an unstable band of sediment-laden saltwater, i.e., the so-called interface layer, sitting between the muddy freshwater and the underlying clear saltwater. This phenomenon has been experimentally observed by Hoyal et al [1999b], Parsons et al [2001], and Blanchette and Bush [2005] and examined through linear stability analysis by Burns and Meiburg [2012] and Yu et al [2013] and Direct Numerical Simulation (DNS) by Yu et al [2014] and Burns and Meiburg [2015]. A few defining characteristics of the settlingdriven mechanism are the general creation of the interface layer below the initial stratification contact [Hoyal et al, 1999b], the onset of Rayleigh-Taylor generated plume like structures, asymmetry in the downward and upward interface motions, and the overall larger length scales of the instabilities and instabilities spacing (centimeter scale) compared to the double-diffusive generated fingering (millimeter scale) [Hoyal et al, 1999b;Blanchette and Bush, 2005;Burns and Meiburg, 2012;Yu et al, 2013;Burns and Meiburg, 2015;Yu et al, 2014].…”

“…This phenomenon has been experimentally observed by Hoyal et al [1999b], Parsons et al [2001], and Blanchette and Bush [2005] and examined through linear stability analysis by Burns and Meiburg [2012] and Yu et al [2013] and Direct Numerical Simulation (DNS) by Yu et al [2014] and Burns and Meiburg [2015]. A few defining characteristics of the settlingdriven mechanism are the general creation of the interface layer below the initial stratification contact [Hoyal et al, 1999b], the onset of Rayleigh-Taylor generated plume like structures, asymmetry in the downward and upward interface motions, and the overall larger length scales of the instabilities and instabilities spacing (centimeter scale) compared to the double-diffusive generated fingering (millimeter scale) [Hoyal et al, 1999b;Blanchette and Bush, 2005;Burns and Meiburg, 2012;Yu et al, 2013;Burns and Meiburg, 2015;Yu et al, 2014]. Further key observations regarding settling-driven instabilities have been that (1) the thickness of the interface layer at the commencement of downward convection tends to thicken as concentration goes down [Hoyal et al, 1999b], (2) that the spacing between points of downward convection tends to also be inversely related to concentration [Hoyal et al, 1999b;Yu et al, 2013], and (3) that the diameters of the instabilities may increase with concentration or sediment settling velocity [Yu et al, 2013].…”

“…Double-diffusive fingering can also occur in thermally stratified systems with warm suspensions of sediment overlying cooler clear water [Houk and Green, 1973;Green, 1987;Hoyal et al, 1999a;Parsons et al, 2001]. Key in the development of double-diffusive fingering for suspensions of sediment is that the sediment in the buoyant layer settles very slowly so that substance diffusion, and not particle settling, is primarily responsible for changes in the vertical density profiles [Burns and Meiburg, 2012;Yu et al, 2013;Burns and Meiburg, 2015;Yu et al, 2014]. Within the band of conditions conducive to double diffusion, transport of sediment within the doublediffusive fingers can be a significant contribution to the total downward sediment flux [Hoyal et al, 1999a].…”

“…More recently, the studies of Meiburg [2012, 2015] and Yu et al [2013Yu et al [ , 2014 have been particularly helpful in understanding key differences in initial conditions that will lead to the onset of doublediffusive or settling-driven Rayleigh-Taylor or leaking instabilities in coastal settings. Both research groups used linear stability analysis to examine the first order instability growth rates under a spectrum of initial conditions.…”