Abstract

We present a new formulation of the bedload sediment flux probability distribution. Individual particles obey Langevin equations which 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 grains. This work provides a statistical mechanics description for the fluctuations and observation-scale dependence of sediment transport rates.

Highlights

  • We present a new formulation of the bedload sediment flux probability distribution

  • We provide a stochastic formulation of the bedload flux based directly on grain-scale mechanics

  • 20 The original description of bedload displacement is due to Einstein, who calculated bedload displacement as a random sequence of rests interrupted by instantaneous steps (Einstein, 1937)

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Summary

Introduction

Bedload transport refers to conditions when grains bounce and skid along the riverbed (Church, 2006). Particle-based, stochastic approaches have been developed from which mean values, probability distributions, and averag ing scales can all be obtained (e.g. Ancey and Pascal, 2020; Turowski, 2010). These approaches provide a more complete description of bedload transport than classic descriptions (e.g. Kalinske, 1947; Bagnold, 1966). Lisle et al (1998) and Lajeunesse et al (2017) improved Einstein’s approach by promoting his instantaneous steps to intervals of motion with constant velocity. Their approach can be summarized with the stochastic equation x (t) = V σ(t),

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