(1) Tracer waiting times and the steady-state evolution of a granular bed
Raleigh L. Martin (*1), Prashant K. Purohit (2), Douglas J. Jerolmack (1)
1. University of Pennsylvania, Department of Earth and Environmental Science
2. University of Pennsylvania, Department of Mechanical Engineering and Applied Mechanics
In bed load sediment transport, particles follow trajectories that alternate between motion and rest. Knowing the distribution of waiting times – the durations of particles in the resting phase – is vital for relating particle tracer studies to bulk sediment motion and bed evolution. Here, we report on laboratory experiments to determine the origin of the tracer waiting time distribution. In the experiments, we tracked the evolution of bed of glass spheres, contained within confined (two-‐ dimensional) channel, that were driven by a steady fluid stress and particle flux. We show that the granular bed evolution resembles an Ornstein-‐Uhlenbeck (O-‐U) process; i.e. an advection-‐diffusion process with tendency to revert to a central value. Monte-‐Carlo simulations of the O-‐U process yield bed surface return times that closely follow the power-‐law bed particle waiting time distribution. The O-‐U process is determined by two parameters. The diffusion parameter increases linearly with particle flux, while the advection parameter is roughly constant for all experiments in our system.