Longitudinal dispersion in laboratory and natural streams

Creators: Fischer, Hugo B.

Abstract

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uniformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream. Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required. Large values of the dimensionless dispersion coefficient D / rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio. A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments. Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington. Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factor of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.

Additional Information

© 1966 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. To Dr. Norman H. Brooks, who suggested this project and was throughout a source of constant and kind advice, assistance, and encouragement, the writer expresses his deepest gratitude. The writer also wishes to thank Dr. Vito A. Vanoni and Dr. Fredric Raichlen for their continuous advice and assistance. For his assistance and patient instruction in building the experimental set up, the writer is deeply indebted to Mr. Elton F. Daly, supervisor of the shop and laboratory. Appreciation is also due Mr. Robert L. Greenway, who assisted with construction of the apparatus; Mr. Leonard A. Fisher, who assisted in performing the experiments and analyzed much of the data; Mr. Ronald Handy, who prepared the drawings; Mrs. Patricia A. Rankin, who typed the manuscript; Mr. Frederick A. Wild, who constructed the conductivity probes; and Mr. Carl T. Eastvedt, who took all of the laboratory photographs. The field experiments were carried out by the U. S. Geological Survey in cooperation with the Municipality of Metropolitan Seattle, as part of a project of the Washington District of the Water Resources Division under Mr. L. B. Laird, District Chief and Mr. J. F. Santos, Project Chief. The writer expresses his appreciation to the many members of the district staff who participated with him in data collection and analysis. Most of the drawings and photographs in Chapter VI were kindly supplied by the Washington District office. The writer's study was supported by fellowships received under the National Defense Education Act (1962-65) and from the Fannie and John Hertz Foundation (1965-66). The writer wishes to thank the U. S. Geological Survey for payment of laboratory research expenses under terms of Memorandum of Agreement No. 14-08-0001-10059 between the Geological Survey and the California Institute of Technology, under which the writer was a Research Participant. Except for the field studies, the research was performed in the W. M. Keck Laboratory of Hydraulics and Water Resources at the California Institute of Technology. This report is a minor revision of a thesis of the same title submitted by the writer in May 1966, to the California Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering.

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