For each combination of
input parameters (settling velocity, flow height, Reynolds number, and slope) we modeled 10 successive flows in hope
of capturing the characteristic upslope migration that has been observed in such features. In the simulations, bottom
shear stress (and thus entrainment, which is modeled as being proportional to shear stress to the 5th power) is high at
the flow front and drops off rapidly. However, shear stress then increases again several times behind the flow front.
This behavior appears to be related to the formation of Kelvin-Helmholtz instabilities at the upper interface of the flow
(see figure 2). Our baseline simulations were performed with Re = 2, 000, us = 0.01, and slope = 0.04 (see figure 3).
In this series of flows, several upslope migrating waveforms developed on the initially flat ramp. Two locations were
significantly net erosive: the top of the ramp and about halfway down the ramp. We now compare this baseline case
against several others, in each of which one parameter was changed while keeping the others constant.