Two-phase model for sand transport in sheet flow regime

We introduce a two-phase model for sand transport in sheet flow regime. This model uses a collisional theory and a k - epsilon fluid turbulence closure to respectively model the sediment and fluid phase stresses. The sediment stress closure adopts a balance equation of sediment particle fluctuation energy based on kinetic theory that incorporates two-way interactions between fluid and sediment phases. The fluid turbulence closure also considers the two-way interaction between fluid turbulence and sand particles. Model-data comparisons for the sheet layer for oscillatory flows in a U-tube and for open channel flows demonstrate the model's predictive skill. For steady open channel flows the fluid phase velocity follows closely the law of wall (i.e., the log-profile) in which the von Karman constant is reduced and the equivalent roughness is increased, compared to the clear fluid flow conditions. The model also provides information in the near-bed region where the transition from the solid-like to the fluid-like behavior of sediment particles is resolved and both the bed load layer thickness and bed load transport rate can be evaluated. For unsteady flows, this model can predict time evolutions for sediment transport throughout the water column.