On bedload particle deposition and hop statistics

Understanding the statistics of bedload particle motions is of great importance. To model the hop events defined as trajectories of particles moving successively from the start to the end of their motions, recently, Wu et al. (Water Resour Res, 2020) have successfully performed individual-based simulations according to the Fokker–Planck equation for particle velocities. However, analytical solutions are still not available due to (i) difficulties in treating the velocity-dependent diffusivity, and (ii) a knowledge gap in incorporating the termination of particle motions for the equation. In the latest work (Wu et al., J Fluid Mech, 2023), we have specified a Robin boundary condition representing the deposition of particles; and devised a variable transformation to deal with the velocity-dependent diffusivity. The original bedload transport problem is thus found to be governed by the classic equation for the solute transport in tube flows with a constant diffusivity after the transformation. By solving the spatial and temporal moments of the governing equation, we have investigated the influence of the deposition rate on three key characteristics of particle hops. Importantly, we have related the deposition rate to the mean travel times and hop distances, enabling a direct determination of this physical parameter based on measured particle motion statistics. The analytical solutions are validated by experimental observations with different bedload particle diameters and transport conditions.