Quantification of probabilistic concentrations for mixed-size sediment particles in open channel flow

The Rouse equation is a well-known deterministic model for suspended concentrations. However, the transport of sediment particles is influenced by several random variables, such as non-uniform sediment size and turbulence structure. Experiments have demonstrated that the stochastic characteristics of turbulence structure, such as ejections and sweeps, can cause fluctuations in sediment concentrations. A new method is proposed to quantify the probabilistic sediment concentrations. In this study, the multiple-state discrete-time Markov chain and stochastic particle tracking model were used to simulate sediment transport with spatially and temporally varying probabilistic concentrations under the stochastic turbulence structure. Point estimate methods were adopted to estimate the variability of non-uniform sediment sizes. The proposed model was implemented for three cases. In the first case, the proposed model was validated against the experimental data. In the second case, spatial and temporal concentrations at high and low Rouse numbers with mean and non-uniform sediment sizes were compared. The result demonstrates that in the prediction with mean sediment sizes, the sediment concentration is overestimated near the bed, and the advection of the sediment concentration in the x-direction is underestimated. In the last case, higher-order statistical moments of the fluctuating concentrations were estimated through simulations using the proposed model. Simulation results conducted using the proposed method were compared with experimental data. The results revealed that the prediction results based on the proposed model are in good agreement with experimental data.