The paper presents a simple mathematical model for sediment transport in straight alluvial channels. The model, which is based on physical ideas related to those introduced by Bagnold (1954), was originally developed in two steps, the first describing the bed load transport (Engelund 1975) and the second accounting for the suspended load (Fredsøe and Engelund 1976). The model is assumed to have two advantages as compared with empirical models, first it is based on a description of physical processes, secondly it gives some information about the quantity and size of the sand particles in suspension and the bed particles.
The stability of a sand bed in an alluvial channel is investigated by a two-dimensional mathematical model, based on the vorticity transport equation. The model takes account of the internal friction and describes the non-uniform distribution of the suspended sediment. It turns out that the inclusion of the friction and of a definite model of the sediment transport mechanism leads to results rather different from those obtained previously by potential-flow analysis.
The paper describes a hydrodynamic stability analysis of the flow in an alluvial channel in which dunes have developed along the bed. The purpose is to develop a mathematical model describing the three-dimensional flow leading to instability of an originally straight channel. The model offers an explanation of the fact that some channels tend to meander, others to braid.
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