An Empirical Validation of Channel Geometry Determined by Threshold Shear Stress

All rivers share common variables that influence their overall shape, but while the patterns that form gravel-bedded rivers are well-defined, less is known about those of fine-grained rivers. From testing by Dunne & Jerolmack, determinants of a sand-bedded river channel's hydraulic geometry were shown to be, to a first order, a combination of water discharge, slope and substrate grain size. For channels with cohesive banks, we surmise that bankfull width and depth is a function of threshold shear stress - in essence, that sand-bedded channels are threshold channels. The specific degrees to which width or depth are determined by discharge or substrate cohesiveness require further exploration. In this project, we systematically demonstrate in a lab-controlled environment that the width and depth of fine-grained alluvial channels are largely determined by substrate cohesiveness and fluid discharge. To validate this relation, we created sand-bedded half-channels in a stream table containing various mixtures of sand and clay as a means of varying cohesion. We evolved these channels to steady state, wherein the average width was no longer changing over time. For each substrate, the discharge rate was varied by a factor of four, both with and without sediment supply. The cross-sections of the resulting threshold channel were then analyzed to obtain an average width and depth, to a resolution of 0.1 microns. The addition of more clay resulted in a channel profile that was narrower and deeper than one with less-cohesive substrate. This, coupled with the fact that these channels were at threshold, seemed to support the notion that hydraulic geometry was controlled by the threshold shear stress of the cohesive material. To corroborate these findings, particle image velocimetry (PIV) was used to determine the time-averaged flow velocity for each channel using floating tracers. Current results suggest that shear stress, when derived from this flow velocity, scales with the cohesiveness of our substrate.