Statistical description of sediment transport experiments

Abstract

A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep twodimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion ͑rest, rolling, or saltating motion͒, and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein's theory on sediment and derived the statistical properties ͑probability distribution and autocorrelation function͒ of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

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.…”

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

“…In Einstein-like theories, particles are entrained when the drag/lift force exerted by the water stream exceeds the resisting force (weight and bed friction) of a stationary particle (see below), and there is no collective entrainment (µ = 0). This results in a purely Poissonian representation of entrainment (Lisle et al 1998;Papanicolaou et al 2002;Ancey et al 2006), which reflects the erosive action of water only and is independent of the number of particles previously entrained. It implies that the total number of moving particles varies little with time, in conflict with experimental and field observations .…”

“…Another problem is the proper definition of the characteristic time of entrainment and deposition rates, controversy about which has led to several attempts to refine Einstein's original formulation (Paintal 1971;Laursen 1999;Lopez & Garcìa 2001;Kleinhans & van Rijn 2002;Charru, Mouilleron & Eiff 2004;Cheng 2004;Cheng, Tang & Zhu 2004). Other aspects, such as the abnormal diffusion of bed particles or wide fluctuations in the solid discharge, seriously conflict with the predictions of Einstein-like theories (Nikora et al 2001(Nikora et al , 2002Ancey et al 2006)-both field and laboratory experiments have revealed that the instantaneous solid discharge is frequently three to four times higher than its mean value (Kuhnle & Southard 1988;Lisle 1989;Böhm et al 2004), suggesting that the probability density functions of the transport-rate records have a thick tail and thus depart from the expected Gaussian behaviour. This can be seen as the hallmark of collective motions (Sornette 2000); if so, it also undermines any mean-field approximation in which cooperation between particles is unaccounted for.…”

“…In Einstein's theory, sediment transport results from the imbalance between entrainment and deposition. Intermittency in particle motion is usually taken into account by treating it as a two-state Markov process (Lisle et al 1998;Papanicolaou et al 2002;Ancey et al 2006). A severe shortcoming of existing models is that they give unrealistic solid discharge fluctuation distributions; for instance, they predict that the solid discharge gently fluctuates around its mean value for equilibrium flow conditions, whereas experiments reveal the existence of wide and frequent fluctuations .…”

A Lévy Process whose Jumps are Dragged by a Spherical Dynamical System

“…Owing to the importance of sedimentation processes in industry, environmental research, and civil engineering, the transport of particles in fluid flows is a problem that is under constant investigation in physics, engineering, and mathematics. Probabilistic models for sedimentation based on random walks and simple Markov processes can be found, for example, in Pickard and Tory (1977), Gani and Todorovic (1983), Gani (1988), and Ancey et al (2006).…”