Viscous stratified flow towards a line sink
Creators: name: Koh, Robert C. Y.
Publisher: name: California Institute of Technology
Year: 1964

description: A theoretical and experimental investigation has been made for the problem of two-dimensional, viscous, incompressible, steady, slightly-stratified flow towards a line sink. The analytical solution was obtained from the Navier Stokes equations, the continuity equation, and the diffusion equation by making a boundary-layer-type assumption and by using a small perturbation technique based on a perturbation parameter proportional to the sink strength q. The effects of viscosity, diffusivity, and gravity have been included while the inertia effect is neglected in the zeroth order solution. The solution indicates that there exists a withdrawal layer which grows in thickness with the distance x from the sink at the rate x^(1/3) and that the velocity distributions u(y) are similar from one station x to another.
Twenty-five tank experiments were performed using water stratified by means of either salt or temperature. Detailed measurements of the velocity field were made by means of photographs of vertical dye lines. The experiments verify the shape of the velocity profiles as well as their similarity in x as predicted by the theory. 
The applicability of these results to the problem of selective withdrawal from a reservoir is discussed and compared with nonviscous solutions by Yih (6) and Kao (7).
description: © 1964 W. M. Keck Laboratory of Hydraulics and Water Resources. January 1964.

The writer would like to express his gratitude for the guidance and advice offered by Professor Norman H. Brooks throughout the course of this investigation. He is also indebted to Professors Donald R. F. Harleman and Vito A. Vanoni for valuable criticisms of many aspects of the research. The financial assistance received from the following fellowships by the writer during his period of graduate study is gratefully acknowledged: 1961-62 (academic year), Corning Glass Works Foundation Fellowship in Engineering; 1962 (summer), Woodrow Wilson Fellowship;
1963-64 (first term), Gillette Paper-Mate Fellowship in Engineering. The laboratory investigation was supported from September, 1962 through 1963 by Research Grant WP-00428 from the National Institute of Health, United States Public Health Service. The experiments were
carried out in the W. M. Keck Laboratory of Hydraulics and Water Resources at the California Institute of Technology.
For their invaluable help in the design and construction of the laboratory equipment, the writer wishes to thank Mr. Elton F. Daly and Mr. Robert L. Greenway. For his help both in the laboratory and in analyzing the data, the writer wishes to express his gratitude to Mr. Loh-nien Fan.
This report is a minor revision of a thesis of the same title submitted by the writer in December, 1963, to the California Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mechanics. For her assistance in making the modifications and overseeing the publication of the present version of the work, the writer wishes to thank Mrs. Shirley Graham.