A probabilistic description of the bed load sediment flux: 2. Particle activity and motions

Abstract

[1] High-speed imaging of coarse sand particles transported as bed load over a planar bed reveals that the particle activity, the solid volume of particles in motion per unit streambed area, fluctuates as particles respond to near-bed fluid turbulence while simultaneously interacting with the bed. The relative magnitude of these fluctuations systematically varies with the size of the sampling area. The particle activity within a specified sampling area is distributed in a manner that is consistent with the existence of an ensemble of configurations of particle positions wherein certain configurations are preferentially selected or excluded by the turbulence structure, manifest as patchiness of active particles. The particle activity increases with increasing bed stress far faster than does the average particle velocity, so changes in the transport rate with changing stress are dominated by changes in the activity, not velocity. The probability density functions of the streamwise and cross-stream particle velocities are exponential-like and lack heavy tails. Plots of the mean squared particle displacement versus time may ostensibly indicate non-Fickian diffusive behavior while actually reflecting effects of correlated random walks associated with intrinsic periodicities in particle motions, not anomalous diffusion. The probability density functions of the particle hop distance (start-to-stop) and the associated travel time are gamma-like, which provides the empirical basis for showing that particle disentrainment rates vary with hop distance and travel time.

Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories

“…The distribution of the durations of individual jumps in Fig. 4b resembles a gamma-distribution shape and it quantitatively agrees with the experimental data of Roseberry et al [18]. Considering the histogram in Fig.…”

“…Furthermore, recent studies highlighted that the scaling behavior within a particular scale range as well as the boundaries between the ranges may depend on specific transport conditions or motion modes [5,10,14,18,22]. For instance, the transition from the intermediate scale range to the global range, expressed in terms of tu à =d (t is time, u à is friction velocity, d is particle diameter) has been found to vary from tens [14,17] to hundreds [3,22].…”

Bedrock incision by bedload: insights from direct numerical simulations

“…The bedload flux then reaches a relatively steady value: from this moment we consider that the system is in the permanent regime. Let us note that we still observe relatively large fluctuations of the bedload flux, consistent with what has been observed experimentally (see, for instance, Böhm et al, 2004, andAncey et al, 2006), and which motivated stochastic approaches to bedload transport on top of a sediment layer ( Roseberry et al, 2012;Ancey and Heyman, 2014;Fan et al, 2014). However, we will not investigate these fluctuations in further detail and in the rest of the discussion all results are computed in the permanent regime and only concern the average values of the sediment and energy fluxes.…”

Dynamics and mechanics of bed-load tracer particles

“…Here it should be noted that the above formulations for bed load particle flux both require averaging the measured quantities over yet-undetermined timescales (Ancey, 2010;Furbish et al, 2012b). For steady turbulent flows in the laboratory, the particle velocity and step length have been shown to scale linearly with the excess shear velocity (U * − U * c ) (Fernandez Luque and Van Beek, 1976;Lajeunesse et al, 2010;Roseberry et al, 2012;Martin et al, 2012), where U * = √ ρτ b is the shear velocity (m s −1 ), τ b is the basal shear stress, ρ is the fluid density (1000 kg m −3 ), and U * c (m s −1 ) is the threshold shear velocity for initiation of sediment motion. Specifically, Lajeunesse et al (2010) found that the modal particle step length scales as…”

“…A particle step is defined as the distance the particle is transported from entrainment to deposition, and the rest duration is the time between deposition and subsequent entrainment. The motion of particles in bed load transport is comprised of sliding, rolling, or short hops called saltations (Drake et al, 1988), where the travel time is generally much shorter than the rest duration (Lajeunesse et al, 2010;Martin et al, 2012;Furbish et al, 2012b, a;Roseberry et al, 2012). For near-threshold bed load transport, in which only bed surface particles are mobile, bed load flux may be described as the product of the particle velocity and surface density (particles/area) of moving grains (Bridge and Dominic, 1984;Wiberg and Smith, 1989;Parker et al, 2003;Lajeunesse et al, 2010;Furbish et al, 2012b), or similarly the product of the particle entrainment rate and the average particle step length (Einstein, 1950;Wilcock, 1997a;Wong et al, 2007;Ganti et al, 2010;Furbish et al, 2012b).…”