Instability and river channels

Abstract

A linearized stability analysis of the flow of water in a channel with a loose bed and straight banks is described. It is assumed that the wavelength of the perturbations, which develop into meanders or braids, is longer than the width of the channel. It is therefore long compared with the ripples or dunes which cover the bed of such a channel and whose wavelength is shorter than the width of the channel. The latter need be allowed for only as roughness elements creating resistance. The variation of resistance to flow and rate of transport of bed material with velocity are discussed briefly and taken into account. Instability is interpreted as leading to a meandering or braided channel and it is shown that all practicable channels are unstable. Wavelengths calculated for channels expecte to meander are compatible with those given by Inglis's empirical rule and wavelengths calculated for channels which become braided are approximately the same as those observed.