Erosion of a granular bed driven by laminar fluid flow

Abstract

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid 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 refractive indices of the fluid and the glass beads are matched and the cell 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 non-dimensional ratio $\theta$ of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for $\theta >{\theta }_c$. We find that the Shields criterion describes the observed relationship $h_r\propto Q^{1/2}$ when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of $\theta$ yields a collapse of the measured Einstein number $q^{\ast }$ to a power-law function of $\theta -{\theta }_c$ with exponent $1.75\pm 0.25$. The dynamics of the bed height relaxation are well described by the power law relationship between the granular flux and the bed stress.

12 pages, 5 figures

References in corpus (1)

• Multi-scale clustering in granular surface flows

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