Stationary waves and antidunes in alluvial channels
Creators: name: Kennedy, John F. (John Fisher)
Publisher: name: California Institute of Technology
Year: 1961

description: 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.
description: Final Report to U. S. Department of Agriculture. Agricultural Research Service Contract USDA-12-14-100-995(41). 

This project was carried out under the general supervision of Professors Vito A. Vanoni and Norman H. Brooks. The writer would like to express his appreciation for the guidance, generous assistance, and valuable criticism which they offered throughout the course of this investigation. 

The writer is also indebted to the following persons for their contributions to the program: Mr. Douglas Christman, Mr. David Butterfield, and Mr. Robert C. Y. Koh for their assistance in performing the experiments, reducing the data, and preparing figures for this report; Mr. Elton F. Daly and Mr. Robert Greenway for modifying the flumes and building the manometer board and other miscellaneous apparatus; Mr. Carl Eastvedt for doing the photography; and Mrs. Barbara Hawk and Mrs. Joann Dodd for their assistance in preparing this report for reproduction. 

In addition, the writer wants to thank Mr. Herb Osborne, Mr.
Fred Long, and Mr. Robert Piest of the Agricuitural Research Service, Oxford, Mississippi, for collecting, assembling and transmitting much of the field data on antidunes which is presented in table 5-3. 

Most of the material presented in this report was submitted by the writer to California Institute of Technology in 1960 in partial fulfillment of the requirements for the Ph.D. degree (31).
description: Submitted - TR000067.pdf