Kao, Timothy W. (1964) Stability of two-layer stratified flow down an inclined plane. W. M. Keck Laboratory of Hydraulics and Water Resources Report, 8. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechKHR:KH-R-8
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Abstract
The stability of flow down an inclined plank has been investigated for the case of a stratified fluid system consisting of two layers of viscous fluid of different densities. This problem is an extension of the works of Benjamin and Yih for a homogeneous fluid; thus their results are a special case of the solution for this more general problem. Asymptotic cases for long and short wave-length disturbances are considered, and the neutral stability curve is estimated. Reynolds numbers for the bifurcation point of the neutral curve are found for various ratios of density and depth of the two layers. For long waves, shear wave instability is also studied and is found to be damped. It is found that the addition of another film of fluid of lighter density over the original film destabilizes the original free surface disturbances. It is hoped that this work will bear on problems of film flow stabilizing techniques, and will also be of interest in the study of the stability of undercurrents in reservoirs.
| Item Type: | Report or Paper (Technical Report) | ||||
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| Additional Information: | © 1964 W. M. Keck Laboratory of Hydraulics. California Institute of Technology. The author wishes to thank Professor N. H. Brooks for his encouragement during the course of this investigation. He is also indebted to Mr, Loh-Nien Fan, Graduate Research Assistant, who wrote the FORTRAN IV programs for the numerical computations of the curves in Figures 3 through 7. The computations were executed on an IBM 7094 computer of the Booth Computing Center of the California Institute of Technology. The project was supported by U. S. Public Health Service Grant WP-00428. The author also wishes to thank Mrs. Pat Rankin for her typing service. | ||||
| Group: | W. M. Keck Laboratory of Hydraulics and Water Resources | ||||
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| Series Name: | W. M. Keck Laboratory of Hydraulics and Water Resources Report | ||||
| Issue or Number: | 8 | ||||
| DOI: | 10.7907/Z9M043B1 | ||||
| Record Number: | CaltechKHR:KH-R-8 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechKHR:KH-R-8 | ||||
| Usage Policy: | You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format. | ||||
| ID Code: | 25983 | ||||
| Collection: | CaltechKHR | ||||
| Deposited By: | Imported from CaltechKHR | ||||
| Deposited On: | 14 Jun 2004 | ||||
| Last Modified: | 03 Oct 2019 03:10 |
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