In field-scale modeling, when the resuspension of sediment is modeled using a hydrodynamic model, a standard and common approach is to add a resuspension flux as the bottom boundary condition in the transport model. In this study, we show that the way of simply imposing an empirical bottom erosion formula as the flux is actually unrealistic. Its inability to stabilize the sediment concentration can cause excessive suspension fluxes in some extreme cases. Moreover, we present a modified erosion/deposition formula to model the resuspension of sediment. The formulation is based on volume conservation in the presence of erosion/deposition near the bottom. By taking into account the prescribed dry density of the bed material, the proposed formulation is able to produce realistic near-bed concentrations while ensuring model stability. The formulation is then tested in a one-dimensional vertical model and field modeling cases using a three-dimensional coastal circulation model. We show that the modified formulation is particularly important in modeling mud resuspension subject to the large bottom stress, which can be a result of waves or a strong river discharge.
The stability of the interface formed by fine suspended particles is studied through linear stability analysis. Our derivation using the regular perturbation expansion with respect to the particle’s settling velocity shows that the unstable modes are independent of the gravitational settling of individual particles. These modes can be obtained from the six-order ordinary differential equation obtained from the analysis of zero-order quantities. In addition to the four boundary conditions applied at the interface in the traditional Rayleigh-Taylor problem in the semi-infinite domain, two conditions based on the continuity of the concentration of the background stratification agent and its gradient are introduced. Our stability results show transition of modes from a small value in a regime of Rayleigh-Taylor instability to the large values of double-diffusive convection when the background density stratification becomes increasingly significant. In the latter case, our analysis shows growth of small perturbations with dominant wavelengths scaled by the double-diffusion length scale. The transition of unstable modes depends on the density ratio, the Prandtl number of the stratification agent, and the viscosity ratio between the two fluid layers. The analysis is further confirmed by the results from the direct numerical simulation.
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.
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