Characteristics of transverse mixing in open-channel flows
Creators: name: Okoye, Josephat K.
Publisher: name: California Institute of Technology
Year: 1970

description: The transverse spreading of a plume generated by a point source in a uniform open-channel flow is investigated. A neutrally-buoyant tracer was injected continuously at ambient velocity through a small round source at a point within the flow. Tracer concentration was measured in situ at several points downstream of the source using conductivity probes. 

Tracer concentration was analyzed in two phases. 

In Phase I, time-averaged concentration was evaluated, its distribution within the plume determined, and characteristic coefficients of transverse mixing calculated. It was shown that the transverse mixing coefficient varied with the flow level and was highest near the water surface where flow velocity was greatest. In contrast to previous speculation, the ratio of the depth-averaged coefficient of transverse mixing D-_z to the product of the (bed) shear velocity u_* and the flow depth d was not a constant but depended on the aspect ratio γ = d/W, where W = flume width. For laboratory experiments D-_z/u_*d decreased from .024 to 0.093 as γ increased from 0.015 to 0.200. 

In Phase II, the temporal fluctuation of tracer concentration was studied in three sections. In the first, the intermittency factor technique was used to delineate three regions of the plume cross section: an inner core where tracer concentration c(t) was always greater than the background C_b; an intermittency region where c(t) was only intermittently greater than C_b; and the outer region where C_b was never exceeded. Dimensional analysis furnished universal curves for prediction of the geometric characteristics of the three regions. In the second section, the entire plume, at a fixed station, was treated as a fluctuating cloud. Variances characterizing the fluctuation of the plume centroid and the variation of the plume width were calculated and compared. In the third section, the intensity and probability density of the concentration fluctuations at fixed points were calculated. The distribution of the peak-to-average ratio was also determined. 

Finally the results of the two phases of study were interrelated to evaluate their contributions to the transverse spreading of the plume.
description: The writer expresses his deepest gratitude to his adviser, Dr. Norman H. Brooks, who suggested this project and was constantly a source of unwavering advice, assistance, and encouragement. 

The writer also wishes to thank Dr. Vito A. Vanoni and Dr. Frederic Raichlen for their kind advice and assistance, and Dr. E. John List for his comments during the writing of the thesis. 

For his invaluable assistance and instruction in the design and construction of the laboratory equipment, the writer is especially indebted to Mr. Elton F. Daly, supervisor of the shop and laboratory. The assistance of Robert L. Greenway in the construction of the apparatus is also much appreciated. 

The writer also wishes to thank Mr. Carl A. Green, Jr., for the preparation of the drawings; Mr. Carl T. Eastvedt for the photography; Mrs. Alrae Tingley for typing the manuscript; and Mrs. Patricia A. Rankin and Mrs. Arvilla F. Krugh for their helpful secretarial aid. The writer also appreciates the efforts of the laboratory assistants: Messrs. Raul Basu, George Chan, Yoshiaki Daimon, Brady Farrand, Edward F. Thompson, W. H. Waggy, Paul T. Wegener, and Mashio Yatsuzuka who performed various duties during the investigation. 

This study was supported by the Federal Water Quality Administration (formerly Federal Water Pollution Control Administration) through Grants No. 16000 DGY and No. 16070 DGY. The experiments were conducted in the W. M. Keck Laboratory of Hydraulics and Water Resources of the California Institute of Technology. 

This report was submitted in November, 1970, as a thesis with the same title to the California Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Environmental Engineering Science.