The mechanics of dunes and antidunes in erodible-bed channels

Abstract

An analytic model of free-surface flow over an erodible bed is developed and used to investigate the stability of the fluid-bed interface and the characteristics of the bed features. The model is based on the potential flow over a two-dimensional, moving, wavy bed with a sinusoidal profile of varying amplitude, and a sediment transport relation in which the transport rate is proportional to a power of the fluid velocity at the level of the bed. By assuming that the dominant wavelength is that for which the rate of amplitude growth is the greatest, expressions are obtained for the wavelength and velocity of the bed features. In addition, conditions for the occurrence of the different configurations, dunes, flat bed, and antidunes, are found from the model. The predicted wavelengths of antidunes and ranges of wavelengths of dunes, and the predicted conditions for change of bed configuration are found to be in good agreement with experimental data. Finally, brief consideration is given to the factors involved in determining the maximum heights of the bed features and surface waves.