Hydraulic Geometry of Threshold Channels

Abstract

The shape and dimensions of the cross section of a straight threshold channel are obtained by numerically solving the momentum balance equation for the fluid and the force balance equation for a sediment particle at the condition of impending motion. The first equation accounts for lateral momentum diffusion from the center of the channel toward its banks, that is caused by Reynolds stresses. The resulting bank profile is accurately described by a fifth‐degree polynomial that is quite different from the cosine, parabolic, or exponential profiles that have been traditionally assumed to represent the shape of a threshold bank. In fact, it is demonstrated here that the cosine and parabolic bank shapes are unstable, while the exponential is overly stable. Equations for the design of threshold channel cross sections are presented. Channel dimensions predicted by these equations are in good agreement with values obtained from laboratory experiments.