In this study, we investigate Rayleigh-Taylor instability in which the density stratification is caused by the suspension of particles in liquid flows using the conventional single-phase model and Euler-Lagrange (EL) two-phase model. The single-phase model is valid only when the particles are small and number densities are large, such that the continuum approximation applies. The present single-phase results show that the constant settling of the particle concentration restricts the lateral development of the vortex ring, which results in a decrease of the rising speed of the Rayleigh-Taylor bubbles. The EL model enables the investigation of particle-flow interaction and the influence of particle entrainment, resulting from local non-uniformity in the particle distribution. We compare bubble dynamics in the single-phase and EL cases, and our results show that the deviation between the two cases becomes more pronounced when the particle size increases. The main mechanism responsible for the deviation is particle entrainment, which can only be resolved in the EL model. We provide a theoretical argument for the small-scale local entrainment resulting from the local velocity shear and non-uniformity of the particle concentration. The theoretical argument is supported by numerical evidence. Energy budget analysis is also performed and shows that potential energy is released due to the interphase drag and buoyant effect. The buoyant effect, which results in the transformation of potential energy into kinetic energy and shear dissipation, plays a key role in settling enhancement. We also find that particle entrainment increases the shear dissipation, which in turn enhances the release of potential energy.
[1] The forcing effect of channel width variations on free bars is investigated in this study using a two-dimensional depth-averaged morphodynamic model. The novel feature of the model is the incorporation of a characteristic dissipative Galerkin (CDG) upwinding scheme in the bed evolution module. A correction for the secondary flows induced by streamline curvature is also included, allowing for simulations of bar growth and migration in channels with width variations beyond the small-amplitude regimes. The model is tested against a variety of experimental data ranging from purely forced and free bars to coexisting bed forms in the variable-width channel. The CDG scheme effectively dissipates local bed oscillations, thus sustains numerical stabilities. The results show that the global effect of width variations on bar height is invariably suppressive. Such effect increases with the dimensionless amplitude A C and wave number l C of width variations. For small A C , l C has little effects on bar height; for A C beyond small amplitudes, however, the suppressing effect depends on both A C and l C . The suppressing effect on bar length increases also with both A C and l C , but is much weaker than that on bar height. The global effect of width variations on bar celerity can be suppressive or enhancive, depending on the combination of A C and l C . For smaller l C , the effect on bar celerity is enhancive; for larger l C , bar celerity tends to increase at small A C but decreases for A C beyond small amplitudes. We present herein an unprecedented data set verifying the theoretical prediction on celerity enhancement. Full suppression of bar growth above the theoretically predicted threshold A C was not observed, regardless of the adopted amplitude of initial bed perturbation A. The global effects of width variations on free bars can be quantified using a forcing factor F C that integrates the effects of A C and l C . The suppressing effects on bar height and length are both proportional to F C 2.16; the global effect on bar celerity is, however, a parabolic function of F C .
We conduct numerical simulations using the Eulerian–Lagrangian approach to investigate the formation of the leaking, finger, and stable-settling modes in convective sedimentation when a sediment-laden fluid layer descends through a sharply stratified ambient flow. We show that the temporal evolution of the sedimentation process for the leaking mode can be divided into three stages, including (in temporal order) Rayleigh–Taylor instability, convection, and leaking stages. The presence of sheet-like descending plumes of suspended particles is an important characteristic of the leaking mode, which marks the existence of the leaking stage. For larger particles, the motion is more dominated by gravitational settling and less affected by buoyancy-induced flow motion. The resulting lack of the leaking stage for the larger-particle case leads to persistent finger-like plumes of suspended particles, known as the finger mode. The stable-settling mode occurs when the particles are large and the concentration is dilute such that flow motion due to Rayleigh–Taylor instability has no effect on the particle motion, and the convective motion of suspended particles is insignificant. For the third stage of the leaking mode, which is also the final stationary state, we derive the criterion for the occurrence of the leaking pattern from a scaling argument of the viscous boundary layer. The criterion is further confirmed by the present simulation results and previous laboratory experiments. Through analysis of the energy budget and the vertical flux, we show that although the settling of individual particles is accelerated, the presence of the sheet-like descending plumes in the leaking mode does not contribute to an efficient settling enhancement compared with the finger mode and the Rayleigh–Taylor instability, i.e., the cases with no background stratification. This implies a negative effect on the settling enhancement for small suspended particles when a stable background density stratification exists. In addition, simulations using the equilibrium Eulerian description for the suspended particles are also conducted to examine the difference between the present Lagrangian particle approach and the conventional Eulerian model.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.