Diffusive Behavior and Statistical Evolution of Sediment Transport From DNS-DEM and Stochastic Models

Abstract

Sediment transport in rivers and channels can be understood as a diffusive phenomenon, where sediment particles separate as they move downstream. This diffusive behavior can be Fickian or anomalous (superdiffusive, subdiffusive, ballistic, etc.), depending on the time evolution of the sediment displacement variance. Many authors have observed transitions from ballistic to Fickian or subdiffusive regimes as the observation timescale increases, aligning with the conceptual model of Nikora et al. (2002), https://doi.org/10.1029/2001wr000513. Despite progress, the mechanisms driving these transitions remain unclear. To investigate them, we simulate a flat-bed channel entraining sediment using Direct Numerical Simulations (DNS) to solve the flow and a point-particle Discrete Element Method (DEM) to resolve particle dynamics, including collisions. The DNS-DEM algorithm is two-way coupled, with the flow responding to particles through a cell-based projection of drag forces. In parallel, we implement stochastic models calibrated from DNS-DEM results, including linear and non-linear advection-diffusion equations and autoregressive Markov models (correlated/non-correlated with Gaussian/non-Gaussian distributions). We study eight cases spanning Shields numbers from 0.03 to 0.85, focusing on the evolution of the mean, variance, skewness, and kurtosis of particle displacement. We observe a ballistic regime at short timescales and near-Fickian at longer ones, though subdiffusion is also present at low Shields numbers. Variance, skewness, and kurtosis approach Fickian behavior as time increases, with convergence rates depending on the Shields number. We find that particle motion correlation-an indirect measure of particle inertia-drives the transition from ballistic to Fickian regimes. In contrast, transitions to subdiffusive states are governed by resting times, not particle inertia.