A probabilistic definition of the bedload sediment flux: Experiments

We analyzed bedload transport through detailed spatial-temporal mapping of sand grains from high-speed images taken during flume experiments. These experiments involved four different average fluid velocities. We tracked individual particles at a time resolution of 1/25th of a second over a total of four seconds for each average fluid velocity. Virtually all particles in motion at the lowest two average fluid velocities were mapped, whereas a random subset of particles were tracked in experiments with the highest two average fluid velocities. Spatial data were used to calculate instantaneous velocities of mobilized grains, the length and duration of complete particle hops, and ensemble averaging of particle activity to compare with theoretical formulations. Instantaneous particle velocities in the stream-wise direction show an exponential-like distribution that terminates near maximum fluid velocity. Velocities in the cross-stream direction are normally distributed about zero. For full particle hops from entrainment to deposition, the hop distance versus travel time is non-linear, and suggests that during short hop durations, the proportion of total travel time grains accelerate and decelerate at entrainment and deposition is greater than particles in motion over longer times. This increases the likelihood that particles with long hop durations will have a higher average velocity than particles with short hop durations. Particle activity over a spatial ensemble indicates that the turbulence structure of the flow drives the spatial variability of transport over short timescales. As turbulence structures (e.g. sweeps) move in the downstream direction, the correlation of particle activity within the ensemble is apparent. Furthermore, we observe in our analysis no evidence of sand grains exhibiting heavy-tail transport behavior.