Analyzing and modeling sub-diffusive transport of bedload along a heterogeneous gravel bed using stochastic and statistical methods

Abstract

Bedload transport is one of the main mechanisms for sediment transport in rivers. Bedload transport may exhibit anomalous dispersion behavior during the formation of clusters on the surface of a heterogeneous river bed, which cannot be quantified by the classical Fick’s law of diffusion. This study simplifies the complex bedload transport process to a “mass-spring-damper” system, which can describe the cluster formation process based on the observed cluster geometry. The simulation results are consistent with the morphology of clusters extracted from the experimental gravel bed in our flume. The level of spatial heterogeneity of individual clusters is characterized to distinguish the planform morphology of each cluster, based on estimation of the Hausdorff-Besicovitch dimension of the cluster area. Trapping of sediment particles during bedload transport on a heterogeneous gravel bed is quantified using a random walk approach and the birth-death emigration-immigration Markov process. Sub-diffusive dynamics of bedload transport is also modeled simultaneously using the Langevin equation that defines statistical properties of bedload sediments. Further analysis indicates that the microscopic stochastic Langevin equation relates to a macroscopic deterministic equation according to the continuous time random walk (CTRW) theory.