Determining the scales of collective entrainment in collision-driven bed load

Abstract

Abstract. Fluvial bed-load transport is notoriously unpredictable, especially near the threshold of motion where stochastic fluctuations in sediment flux are large. Laboratory and field observations suggest that particles are entrained collectively, but this behavior is not well resolved. Collective entrainment introduces new length scales and timescales of correlation into probabilistic formulations of bed-load flux. We perform a series of experiments to directly quantify spatially clustered movement of particles (i.e., collective motion), using a steep-slope 2-D flume in which centimeter-scale marbles are fed at varying rates into a shallow and turbulent water flow. We observe that entrainment results exclusively from particle collisions and is generally collective, while particles deposit independently of each other. The size distribution of collective motion events is roughly exponential and constant across sediment feed rates. The primary effect of changing feed rate is simply to change the entrainment frequency, although the relation between these two diverges from the expected linear form in the slowly driven limit. The total displacement of all particles entrained in a collision event is proportional to the kinetic energy deposited in the bed by the impactor. The first-order picture that emerges is similar to generic avalanching dynamics in sandpiles: “avalanches” (collective entrainment events) of a characteristic size relax with a characteristic timescale regardless of feed rate, but the frequency of avalanches increases in proportion to the feed rate. The transition from intermittent to continuous bed-load transport then results from the progressive merger of entrainment avalanches with increasing transport rate. As most bed-load transport occurs in the intermittent regime, the length scale of collective entrainment should be considered a fundamental addition to any probabilistic bed-load framework.