Bed load transport in turbulent flow at the grain scale: Experiments and modeling

We report an experimental investigation of the motion of bed load particles under steady and spatially uniform turbulent flow above a flat sediment bed of uniform grain size. Using a high-speed video imaging system, we recorded the trajectories of the moving particles and measured their velocity and the length and duration of their flights, as well as the surface density of the moving particles. Our observations show that entrained particles exhibit intermittent motion composed of the succession of periods of flight and periods of rest. During one flight, a particle may go through phases of reptation, during which it moves in nearly persistent contact with the rough bed, and phases of saltation, during which it travels sufficiently high above the bed to reach high velocities. The distributions of longitudinal and transverse particle velocities obey a decreasing exponential and a Gaussian law, respectively. Interestingly, these observations are similar to those previously reported for viscous flows. The experimental results presented here support the erosion-deposition model of Charru (2006) and allow the calibration of the involved coefficients. In particular, noting tau*, the Shields number, and tau*(c), the threshold Shields number, we find that (1) the surface density of moving particles increases linearly with tau* - tau*(c); (2) the average particle velocity increases linearly with tau*(1/2) - tau*(1/2)(c), with a finite nonzero value at the threshold; (3) the flight duration scales with a characteristic settling time with no significant dependence on either tau* or the settling Reynolds number; and (4) the flight length increases linearly with tau*(1/2) - tau*(1/2)(c). The results presented in this paper should provide a valuable physical framework to describe bed form development in turbulent flows.