Probabilistic description of bedload fluxes from the aggregate dynamics of individual grains

Abstract

We formulate the bedload sediment flux probability distribution from the Lagrangian dynamics of individual grains. Individual particles obey Langevin equations wherein the stochastic forces driving particle motions are switched on and off by particle entrainment and deposition. The flux is calculated as the rate of many such particles crossing a control surface within a specified observation time. Flux distributions inherit observation time dependence from the on-off motions of particles. At the longest observation times, distributions converge to sharp peaks around classically expected values, but at short times, fluctuations are erratic. We relate this scale dependence of bedload transport rates to the movement characteristics of individual sediment grains. This work provides a statistical mechanics description for the fluctuations and observation-scale dependence of sediment transport rates.