Diffusive regimes of the motion of bed load particles in open channel flows at low transport stages

The stochasticity of fluid and sediment parameters has been identified as a source of diffusion, particularly anomalous diffusion at different temporal and spatial scales of bed load particle trajectories. Data from two sets of flume experiments are presented, one data set has gravel particle trajectories tracked over a limited area and was used in identifying the influence of different shear stress conditions on diffusive processes. A new experiment was performed using spherical particles moving as bed load in an annular flume in order to address concerns about censorship effects caused by the size of the detection window. An annular flume allowed collection of practically uncensored particle trajectories over longer time period than has been previously possible in the laboratory. Three diffusive regimes were observed at distinct stages of particle motion: (i) ballistic regime at the local range; (ii) Fickian diffusion at the intermediate range; (iii) subdiffusion at the global range. Characteristic time scales separate the regimes and correlate with the mean traveling and resting times of particles. Fickian diffusion in the intermediate range is first recognized as a result of the balance between intermittent weak transport and near-bed turbulence, as first predicted by Nikora et al. (2002, https://doi.org/10.1029/2001WR000513). In the global range, extreme values were observed in the distribution of particle resting times, suggesting that two types of distributions (related to surface motion and vertical mixing) were responsible for the subdiffusion at longer time scales. Diffusion was found to be anisotropic at all stages of particle motion.