Lateral Diffusion of Bedload Transport under Laminar Flow

Abstract:

Lateral sediment transport is a key momentum-exchange mechanism to model equilibrium channel geometry and channel bar evolution. We study sediment transport from a statistical mechanical point of view akin to Furbish et al. 2012. This approach holds promise for linking grain-scale motion to macroscopic transport, but there are few data to definitively develop and test such models. We study an experimental model river, composed of monodisperse acrylic spheres dispersed in silicon oil, driven by a layer of fluid under steady shear. We choose to drive fluid flow in the laminar regime (Re < 1) to suppress fluid turbulence and isolate granular and bed structure controls. We use a refractive-index-matched laser scanning technique to observe the motion of particles at the surface of the bed as well as the particle dynamics below the surface. We study how the probability distribution of displacements varies as a function of distance from the bed surface and as a function of distance to the channel center. In the streamwise direction, in agreement with Furbish et al. 2012, we find that the dynamics can be decomposed into an advection and a diffusion term. In the lateral direction, we find a competition between diffusion and an elastic-like interaction with the bed. We study this lateral stochastic process and find a need to introduce two parameters to quantify this competition. The first parameter describes the tendency for particles to reside near the center of the channel and the second parameter describes the kinetic energy distribution of the particles. We study how the requisite averaging scales and ensemble sizes to achieve statistically convergent parameters, and we explore how these parameters depend on the driving rate.