Plunging criterion for particle-laden flows over sloping bottoms: Three-dimensional turbulence-resolving simulations

摘要

Hyperpycnal flows are observed when the density of a fluid entering into a quiescent environment is greater than that of the ambient fluid. This difference can be due to salinity, temperature, concentration, turbidity, or a combination of them. Over a sloping bottom, the inflowing momentum decreases progressively until a critical stage is reached where the inflow plunges underneath the ambient and flows adjacent to the bed as an underflow density current. In the present work, a new equation is proposed in order to predict the critical depth for plunging, i.e., the plunging criterion. It differs from previous studies since it includes the role of the settling velocity and the bed slope. The high spatiotemporal resolution from twelve original numerical simulations allows us to validate the initial hypotheses established, in addition to numerical and experimental data available in the literature, and good agreement is found between them. A negative value for the mixing coefficient was observed for the first time for the hyperpycnal flow in a tilted channel. This indicates that if the settling velocity of the suspended material is high enough, the submerged flow may lose fluid to the environment (detrainment), instead of incorporating it. The proposed plunging criterion may assist in the design of future experimental or numerical works.