Velocity distribution and bed roughness in high‐gradient streams

Abstract

A model for the velocity field over a poorly sorted bed is derived herein and applied to flow in steep streams with coarse gravel beds. In such streams, large clasts often are comparable in size to stream depth and act as obstacles to the flow. The effect of these obstacles on a flow is estimated by partitioning total stress, proportional to the depth‐slope product, into a purely fluid component and a form‐drag component associated with flow around the obstacles. An eddy viscosity closure is used, with a length scale dependent on both distance from the boundary and wake dimension. Resulting velocity profiles agree well with profiles measured by Marchand et al. (1984) in nine mountain streams in Colorado. Model runs for a range of conditions reveal that the velocity distribution depends primarily on D 84 z and flow depth h ; D 84 z is the length of the vertically oriented axis of clasts at the 84th percentile of the grain size distribution. Calculated values of mean velocity, normalized by shear velocity, are well represented by a simple log linear relationship in terms of relative roughness D 84 / h .