Entrainment and motion of coarse particles in a shallow water stream down a steep slope

Abstract

We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth-death immigration-emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90 % of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10 %, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

Periodic saltation over hydrodynamically rough beds: aeolian to aquatic

“…In other words, the mean motion of the fluid is not enough to sustain the particle transport. Indeed, in that case, turbulence bursts are responsible for the particle motion, which is characterized by intermittency (Ancey et al 2008, Lajeunesse et al 2010, Radice et al 2009, Singh et al 2009). Figure 7.…”

“…Below a certain threshold, the forces that the fluid transmits to the particles are not sufficient to set them in motion. Above the threshold, a few erratic particles are seen to slide, roll and jump, in an intermittent way, associated with the local burst of turbulence (Ancey et al 2008, Drake et al 1988, Lajeunesse et al 2010, Nelson et al 1995, Radice et al 2009.…”

Image processing for the study of bedload transport of two-size spherical particles in a supercritical flow

“…11) is mainly characterized by the collective motion of rolling beads as evidenced by a series of gray streaks. This phenomenon was modeled by Ancey et al (2008).…”

“…All particle trajectories were calculated by image processing ) allowing analysis of the fluctuations of sediment rates as well as the state of movement (rolling or saltation). These exhaustive measurements permitted a thorough statistical description of uniform sediment transport based on stochastic Markovtype processes (Ancey et al , 2008.…”

Advection and dispersion of bedload tracers

“…The likeliness of this event depends on the specific disposition of the surrounding particles. On average, however, the probability of entrainment is a function of macroscopic quantities such as shear stress and grain size 20 (Ancey et al, 2008). Once dislodged, the velocity of a particle fluctuates significantly around its average (Lajeunesse et al, (Bradley et al, 2010;Nathan Bradley and Tucker, 2012;Hassan et al, 2013;Phillips et al, 2013).…”