Title: Erosion of a granular bed driven by laminar fluid flow

Author (Talk): Ashish Orpe, Clark University

Abstract:

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed as a function of fluid flux to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid flux $Q$ flows through the cell. The fluid is index matched to the glass beads and is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest height $h_r$ which depends on $Q$. The Shields threshold criterion assumes that the viscous stress on the bed scaled by the hydrostatic pressure difference across a grain is constant and equal to $\\theta_c$ at threshold. Here we find that the Shields criterion describes the observed relationship $h_r \\propto Q^{1/2}$ when bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of the dimensionless shear stress $\\theta$ yields a collapse of the measured Einstein number $q^*$ to a power-law function of $\\theta - \\theta_c$ with exponent $1.75 \\pm 0.25$.