Estimation of near-bed sediment concentrations in turbulent flow beyond normality

Recent experiments have established that sediment particle motion, especially for particles near the bed, may not follow a normal (Fickian) diffusion behavior. To modify the diffusion equation when the fluctuation velocity is based on a normal distribution is a key research goal. This study represents an attempt to acquire some insight into the particle diffusion behavior by considering the turbulent fluctuation velocity based on bivariate probability distributions and by introducing the stochastic particle alignment into the particle–bed collision process in an open channel. The fluctuation velocity distribution is obtained using the Gram–Charlier expansion, which considers the first four statistical moments of turbulent fluctuation velocity. Fluctuation velocities in both streamwise and vertical directions are generated by conducting correlative Monte Carlo simulations. Moreover, in this study, the stochastic particle alignment composed of random particle sizes on the bed, as well as the particle collision process with random angles of incidence of particles is introduced to the particle collision mechanism. The associated probabilities of particle rebounding then would depend on the conditional probability distribution of the collision height. Particle trajectories simulated based on the saltation model and the random particle-bed collision process can be used to estimate the ensemble mean sediment concentration profile and the ensemble variance of sediment concentrations. In this study, the collision process, sediment concentration, and variance of particle motion are verified using available experimental data. Anomalous diffusion of particles can be observed in this study. In the proposed model, particle diffusion in the streamwise direction is found to be superdiffusive and that in the vertical direction is subdiffusive.