The formation of dunes, antidunes, and rapidly damping waves in alluvial channels

Under the effect of a constant current for a long time, a water channel of infinitely long and constant depth interacting with a uniform sandbed of in finite thickness is used to simulate the formation of dunes, antidunes and rapidly damping waves in alluvial channels. The theory of potential flow is applied to the channel flow, while Blot's theory of poroelasticity is adop ted to deal with erodible bed material. The governing equations, together w ith free surface, bed surface, and far held boundary conditions, form a com plete boundary-value problem without applying empirical sediment discharge formulas as in conventional researches. The comparison of the present resul t with Kennedy's (Journal of Fluid Mechanics, 1963; 16: 521-544) instabilit y analysis not only indicates the appropriateness of the present work, but also reveals the advantage of the present study due to its ability to find all kinds of bed forms (including the rapidly damping waves that Kennedy co uld not fmd) and of solving for the unclear lagged distance delta introduce d in Kennedy's work. Copyright (C) 2001 John Wiley & Sons, Ltd.