Understanding partial bed-load transport: Experiments and stochastic model analysis

•A class of partial bedload transport experiments has been conducted.•The leading front of bedload exhibits transient anomalous scaling rates.•Cluster structures cause coexistence of sub- and super-diffusion of bedload.•A stochastic model is employed to capture the anomalous transport of bedload. The complex dynamics of partial bed-load transport in a series of well-controlled laboratory experiments are explored systematically and simulated by a stochastic model in this study. Flume experiments show that the leading front of bed-load on a 20-m-long, mixed-size gravel-bed moves anomalously, where the transient transport rate of the accelerating front varies with the observation time scale. In addition, observations show that moving particles may experience bimodal transport (i.e., coexistence of long trapping time and large jump length) related to bed coarsening and the formation of clusters on a heterogeneous gravel-bed, which is distinguished from the traditional theory of hiding–exposing interactions among mixed-size particles. A fractional derivative model is finally applied to characterize the overall behavior of partial bed-load transport, including the coexistence of the sub-diffusion and non-local feature caused by turbulence and the micro-relief within an armor layer.