Stationary waves and antidunes in alluvial channels

Abstract

A theoretical and laboratory investigation was made of antidunes and associated stationary waves. The objectives were to determine the factors involved in the formation of antidunes, the characteristics of the stationary waves, and the effects of antidunes and waves on the friction factor and sediment transport capacity of streams. In the potential flow solution for flow over a wavy bed it was hypothesized that the flow shapes the erodible sand bed by scour and deposition to conform to a streamline of the flow configuration for which the energy is a minimum. Under this hypothesis, flow over antidunes is the same as the segment of flow above an intermediate streamline of the fluid motion associated with stationary gravity waves (waves with celerity equal and opposite to the flow velocity) in a fluid of infinite depth. For a velocity V the wave length, L, is given by L = (2*pi*V^2)/g and waves break when their height reaches 0.142 L. Laboratory and field data for two-dimensional stationary waves and antidunes confirmed these relations. For the same velocity, short-crested, three-dimensional waves (rooster tails) have shorter wave lengths than two-dimensional waves. Forty-three experimental runs in laboratory flumes were made for different depths and velocities and bed sands of two different sizes (0.549 mm and 0.233 mm). No general criterion for the formation of antidunes or the occurrence of breaking waves could be formulated because of inadequate knowledge of the complex sediment transport phenomenon. Qualitatively, it was found that for a given sand, the critical Froude number for the occurrence of breaking waves decreased as the depth was increased. Over a certain range of depth and velocity it was found that the flow formed waves and antidunes or was uniform depending on whether or not the flow was disturbed to form an initial wave. Waves that did not break had no measurable effect on the transport capacity or friction factor, but breaking waves increased both of these quantities.