On two-phase sediment transport: Dilute flow

In this paper we present a model describing dilute sediment transport that involves two-phase mass and momentum equations and k - ε equations for the energy of turbulent flow. We apply the model to a steady, uniform, open channel flow and calculate sediment concentration and velocity profiles in two ways. In a semianalytical approach we adopt boundary layer approximations and obtain concentration profiles that improve upon the single-phase Rouse formula [Rouse, 1937]. The improvement is due to the incorporation of dissipation of the flow turbulent energy due to the presence of sediment. In a numerical approach we integrate the time-dependent equations of the model to obtain steady state solutions. The numerical solutions are tested against experimental data and used to check the validity of the boundary layer approximations in the semianalytical approach.