Abstract
Abstract. We use the erosion–deposition model introduced by Charru et al. (2004) to numerically simulate the evolution of a plume of bed load tracers entrained by a steady flow. In this model, the propagation of the plume results from the stochastic exchange of particles between the bed and the bed load layer. We find a transition between two asymptotic regimes. The tracers, initially at rest, are gradually set into motion by the flow. During this entrainment regime, the plume is strongly skewed in the direction of propagation and continuously accelerates while spreading nonlinearly. With time, the skewness of the plume eventually reaches a maximum value before decreasing. This marks the transition to an advection–diffusion regime in which the plume becomes increasingly symmetrical, spreads linearly, and advances at constant velocity. We analytically derive the expressions of the position, the variance, and the skewness of the plume and investigate their asymptotic regimes. Our model assumes steady state. In the field, however, bed load transport is intermittent. We show that the asymptotic regimes become insensitive to this intermittency when expressed in terms of the distance traveled by the plume. If this finding applies to the field, it might provide an estimate for the average bed load transport rate.
Highlights
Alluvial rivers transport the sediment that makes up their bed
Lajeunesse et al (2013) used the erosion–deposition model introduced by Charru et al (2004) to derive the equations governing the evolution of a plume of tracers
The erosion–deposition model introduced by Charru et al (2004) provides an accurate description of this dilute regime in which bed load transport is controlled by the exchange of particles between the sediment bed and the bed load layer
Summary
Alluvial rivers transport the sediment that makes up their bed. From a mechanical standpoint, the flow of water applies a shear stress on the sediment particles and entrains some of them downstream. The flow was constant in this experiment, the tracers still dispersed as they traveled downstream In this case, dispersion resulted from the inherent randomness of bed load transport only. In a recent paper, Lajeunesse et al (2013) used the erosion–deposition model introduced by Charru et al (2004) to derive the equations governing the evolution of a plume of tracers Neglecting velocity fluctuations, they found that the second dispersion process, namely the exchange of particles between the bed load layer and the sediment bed, efficiently disperses the tracers. We discuss the applicability of these results to the field (Sect. 6)
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