A Model for Flow in Meandering Streams

Abstract

Erosion and deposition in streams and tidal channels depend on the divergence of the sediment‐flux field, and this is governed by the distribution of boundary shear stress. As a consequence, erosion arid deposition patterns in such systems are sensitive to spatial variations in boundary shear stress, which in turn, can be induced by the complex interplay between the flow and bed and bank topography. A method whereby variations in boundary shear stress can be calculated is presented herein for flows that are broad in relation to their depth and for which the bed slopes are small. The formal scheme employs a regular perturbation expansion around a zero‐order state that includes vertically integrated, topographically induced convective accelerations. Use of a zero‐order velocity field that includes these accelerative effects yields a model that is applicable to streams with typical bed slopes and channel curvatures, one that can be employed in the majority of situations of interest to geomorphologists, sedimentologists, and hydraulic engineers concerned with fluvial and estuarine systems. In order to verify the model, our calculations are shown to reproduce, with reasonable accuracy, the free‐surface topography and boundary shear stress distribution measured by Hooke (1975) when applied to a channel of the geometry that he investigated. The latter part of the paper describes how the interplay of the various components of flow through a curved channel with bar‐pool topography is affected by the parameters of the problem.