Grain-size distribution and diffusivity of non-uniform sediment in the channel with submerged vegetation

The interaction between aquatic vegetation and sediment is critical for river restoration and ecosystem stability, where accurately predicting non-uniform sediment transport (the dominant mode in natural rivers) is crucial for effective management. However, the most existing numerical models struggle to precisely simulate suspended sediment profiles of non-uniform sediment because it is difficult to describe the interaction of per groups. This study improved the settling velocity formula to quantify particle interactions incorporating relative diameter and geometric standard deviation, and then developed an advanced random displacement model (RDM) for suspended sediment profiles in vegetated channels. The model, validated against analytical solutions and experiments, resolves near-bed discrepancies via settling velocity incorporating hiding-hindering effects. Results reveal strong vertical stratification of non-uniform sediment, leading to a shift in suspended sediment gradation with elevations, that is smaller particles dominate at greater heights due to their increasing relative proportion. The non-uniformity coefficient $\eta ={\left(D_m/D_i\right)}^{1/4}{\sigma }_D^{-1/8}$ (where D_i represents ith group size, D_m and ${\sigma }_D$ are the mean diameter and the geometric standard deviation of non-uniform sediment, respectively) was introduced to quantify the impact of non-uniform sediment to particles. Results show that the non-uniformity coefficient is related to elevations and grain sizes. The Schmidt number S_c, the ratio of turbulence viscosity to sediment diffusivity, was further studied to clarify sediment diffusion characteristics with the effects of non-uniform sediment and submerged vegetation. The results of statistical significance testing indicate that S_c in non-uniform sediment significantly increases compared to that in uniform sediment, corresponding to a 69% increase in S_c, which results from the stratification of different-size sediment and the dominant role of coarse grains in the near-bed regions. The study elucidates the couple effects of vegetation-induced turbulence and particle-size stratification on sediment transport, providing mechanistic insights to inform adaptive strategies for river restoration and ecosystem stability.