The transition from intermittent to continuous bed-load transport arises from merger of "bursty" transport events

Bed-load transport is notoriously unpredictable, in part due to stochastic fluctuations in grain entrainment and deposition. A general statistical mechanical framework has been proposed by Furbish and colleagues to formally derive average bed-load flux from grain-scale motion, and its application requires an intimate understanding of the probabilistic motion of individual grains. Recent work by Ancey et al. suggests that, near threshold, particles are entrained collectively. If so, understanding the scales of correlation is a necessary step to complete the probabilistic framework describing bed-load flux. We perform a series of experiments in a steep-sloped channel that directly quantifies fluctuations in grain motion as a function of the feed rate of particles (marbles). As the feed rate is increased, the necessary averaging time is decreased (i.e. transport grows less variable in time). Collective grain motion is defined as spatially clustered movement of several grains at once. We find that entrainment of particles is generally collective, but that these entrained particles deposit independently of each other. The size distribution of collective motion events follows an exponential decay that is consistent across sediment feed rates. To first order, changing feed rate does not change the kinematics of mobile grains, just the frequency of motion. For transport within a given region of the bed, we show that the total displacement of all entrained grains is proportional to the kinetic energy deposited into the bed by impacting grains. Individual grain-bed impacts are the likely cause of both collective and individual grain entrainment. The 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. At high enough feed rates the avalanches merge, leading to progressively smoother and continuous transport. As most bed-load transport occurs in the intermittent regime, the length scale of collective entrainment should be considered a fundamental addition to a probabilistic framework that hopes to infer flux from grain motion.