Entrainment, motion and deposition of coarse particles transported by   water over a sloping mobile bed
  In gravel-bed rivers, bedload transport exhibits considerable variability in time and space. Recently, stochastic bedload transport theories have been developed to address the mechanisms and effects of bedload transport fluctuations. Stochastic models involve parameters such as particle diffusivity, entrainment and deposition rates. The lack of hard information on how these parameters vary with flow conditions is a clear impediment to their application to real-world scenarios. In this paper, we determined the closure equations for the above parameters from laboratory experiments. We focused on shallow supercritical flow on a sloping mobile bed in straight channels, a setting that was representative of flow conditions in mountain rivers. Experiments were run at low sediment transport rates under steady nonuniform flow conditions (i.e., the water discharge was kept constant, but bedforms developed and migrated upstream, making flow nonuniform). Using image processing, we reconstructed particle paths to deduce the particle velocity and its probability distribution, particle diffusivity, and rates of deposition and entrainment. We found that on average, particle acceleration, velocity and deposition rate were responsive to local flow conditions, whereas entrainment rate depended strongly on local bed activity. Particle diffusivity varied linearly with the depth-averaged flow velocity. The empirical probability distribution of particle velocity was well approximated by a Gaussian distribution when all particle positions were considered together. In contrast, the particles located in close vicinity to the bed had exponentially distributed velocities. Our experimental results provide closure equations for stochastic or deterministic bedload transport models. 
J. Heyman, P. Bohorquez, C. Ancey
physics.flu-dyn