  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 $q^*$ 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.
