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On the generation of surface waves by shear flows. Part 2

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Department of Engineering, University of California, Los Angeles
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Abstract

A previous analysis for the generation of surface waves by a parallel shear flow (Miles 1957 a) is extended by: (a) presenting results based on a more accurate solution of the differential equation; (b) imposing the boundary condition at the surface wave, rather than at the mean surface; and (c) including the dominant viscous term in the complete Orr-Sommerfeld equation. The modification (a) yields an energy transfer somewhat smaller than that predicted previously but of the same order of magnitude as, and in rather better agreement with, observation, while (b) has no effect and (c) only a small effect for gravity waves. The analysis is based on the equations of motion in intrinsic co-ordinates (rather than the usual Orr-Sommerfeld equation) and may be of interest in other problems of hydrodynamic stability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 4 , November 1959 , pp. 568 - 582
Copyright
© 1959 Cambridge University Press

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References

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