Width and Depth Adjustments for Sediment Models of Scour and Deposition

A method is developed for determining the direction and magnitude of channel width and depth adjustments. It could be used in sediment models that simulate scour and deposition. The method is based on quantification of extremal theories such as extremal energy dissipation, extremal sediment efficiency and extremal friction factor. The extremal method is combined with a variational approach to supply the width and depth adjustments. When the width and depth are the only degrees of freedom, two modes of channel adjustment toward equilibrium are predicted; width widening and bed rising on one hand, and width narrowing and bed lowering on the other hand. Therefore, the interrelationship between adjustments in width and depth of alluvial channels toward equilibrium is accounted for correctly. Predictions of channel width at the Yellow River are presented.