A Statistical Description of Particle Motion and Rest Regimes in Open‐Channel Flows Under Low Bedload Transport

Abstract

In the last decade several efforts were devoted to model sediment‐particle transport in rivers as a stochastic process. Experimental observations are therefore needed to validate these models and to provide the correct probability distribution of selected stochastic variables. The kinematics of sand particles is investigated here using nonintrusive imaging to provide a statistical description of bedload transport under incipient motion conditions. In particular, we focus on the alternation between motion (particle steps) and rest regimes to quantify the probabilistic distribution of the particles waiting time, which is suggested by many studies to be responsible for anomalous diffusion. The probability distributions of the particle step time and step length, streamwise and spanwise velocities, acceleration, and waiting time are quantified experimentally. Results suggest that variables describing the particle motion regime are thin‐tailed distributed, whereas the waiting times exhibit a power law distribution. A specific class of waiting times during which the grain is observed to oscillate without a net displacement is classified as active and is analyzed separately from the other, so‐called deep waiting times. The experimental results, obtained under five different transport conditions, describe grain‐scale kinematics and dynamics at different wall shear stress. They provide both a benchmark data set for validating particle‐transport numerical simulation and critical input parameters for the stochastic modeling of bedload transport.

Probability Distributions of Particle Hop Distance and Travel Time Over Equilibrium Mobile Bedforms

“…This value is significantly lower than the threshold velocities adopted by Liu et al. (2019) and Lajeunesse et al. (2010), perhaps because the lower frame rate (30 frames per second in the present study compared with 90 frames per second) allows more precise estimates of frame‐averaged velocity.…”

“…We recognize this issue but do not attempt to solve it here. Instead, we use an approach that is similar to previous studies (Liu et al., 2019) and acknowledge where our results might be sensitive to this choice. Velocity criteria are an objective, reproducible solution to this problem.…”

“…Our analysis assumes that the marginal distributions of particle hop distance and travel time have thin tails such that the mean and the variance are well defined. Although previous studies suggest that this is true for monodisperse sediment undergoing low bedload transport (Fathel et al, 2015;Liu et al, 2019), heavy-tailed distributions of hop distance and travel time are possible if a range of grain sizes are present and the mean hop distance varies with grain size (Ganti et al, 2010). Our experiments involved naturally sorted sediment, which is valuable insofar as we seek to understand Journal of Geophysical Research: Earth Surface natural transport systems.…”

“…The joint probability distribution of particle hop distance and travel time encapsulates the relationship between granular sediment motion and topographic change (Ancey, 2010; Furbish et al., 2012; Nakagawa & Tsujimoto, 1976; Pelosi & Parker, 2014; Tsujimoto, 1978). Considerable attention has been devoted to the problem of discerning the forms of the associated marginal distributions and predicting their parameters or moments under steady, uniform macroscopic flow conditions (Abbott & Francis, 1977; Fathel et al., 2015; Furbish, Fathel, & Schmeeckle 2016; Hosseini Sadabadi et al., 2019; Lajeunesse et al., 2010; Liu et al., 2019). This objective represents an important step toward the development of models for large‐scale fluvial morphodynamics that are consistent with the physics of grain‐scale sediment transport.…”

A velocity-variation-based formulation for bedload particle hops in rivers

“…This progress has mostly involved the assumption of a thin-tailed p.d.f. of hop-distances during the implementation of theoretical (Ganti et al 2010;Lajeunesse, Devauchelle & James 2018;Wu et al 2019a,b), numerical (Fan et al 2014(Fan et al , 2016Pelosi et al 2016) and experimental (Martin, Jerolmack & Schumer 2012;Bradley 2017;Liu, Pelosi & Guala 2019) approaches.…”