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.
STUDY ON HYDRAULIC RESISTANCE AND BED-LOAD TRANSPORT RATE IN ALLUVIAL STREAMS