Viscous Stratified Flow Towards a Line Sink

Citation

Koh, Robert Ching-Yee (1964) Viscous Stratified Flow Towards a Line Sink. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YXY3-GG82. https://resolver.caltech.edu/CaltechETD:etd-09252002-135207

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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 first making a boundary-layer-type assumption and then using a small perturbation technique based on a perturbation parameter proportional to the sink strength q. The effects of the viscosity, the diffusivity, and the 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[superscript 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. Except for scale, this is very similar to the problem of selective withdrawal from a reservoir.

Thesis Files