Two-dimensional sediment transport models for sand-bed rivers

The problem of determining the specific mass flow of sediment entrained by a liquid flow passing above the sand bottom is studied. The boundary-value problem for a two-phase mixture of the liquid and solid particles in the active bottom layer is solved, and a general formula for determining the specific mass flow of sediment is derived. Constraints imposed on the rheological model of a moving mixture, which allow the phenomenological parameter (concentration of particles in the active layer of the mixture) to be eliminated from the model, are found. Within the framework of the proposed rheological model, the equation of riverbed deformations in the case of a sand bottom is obtained.