Stable Channels with Mobile Bed: Formulation and Numerical Solution

Abstract

Natural rivers and streams are observed to maintain stable banks while transporting sediment over a central bed region. The development of a numerical model that accounts for this essential feature of natural rivers and streams is discussed in this paper. The model considers the concept of momentum diffusion, and assumes a channel comprising a flat-bed region and two curving bank regions. The resulting boundary stress distribution is such that boundary particles in the flat-bed region are subjected to stresses great enough to put them in motion, while particles in the bank regions are only in a state of incipient motion. It is the combination of this channel geometry and the phenomenon of momentum diffusion that allows for the successful simulation of the “stable bank, mobile bed” condition experienced by rivers. While this paper emphasizes the theoretical and numerical aspects of the problem, a companion paper deals with the application and verification of the model. It presents design equations and grap...