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Non-linear gravity wave interactions

Published online by Cambridge University Press:  28 March 2006

D. J. Benney
D. J. Benney
Affiliation:
Massachusetts Institute of Technology, Cambridge, Mass.
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Abstract

In earlier papers Phillips (1960) and Longuet-Higgins (1962) have investigated phase velocity effects and possible resonances associated with the interactions of gravity waves. In this note the problem is discussed from a different viewpoint which demonstrates more clearly the energy-sharing mechanism involved. Equations governing the time dependence of the resonant modes are obtained, rather than the initial growth rate as has been found previously.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 4 , December 1962 , pp. 577 - 584
Copyright
© 1962 Cambridge University Press

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References

Benney, D. J. & Greenspan, H. P. 1962 Phys. Fluids. (in the Press).
Bogoliuboff, N. & Mitropolski, Yu. A. 1958 Asymptotic methods of non-linear mechanics Moscow.
Longuet-Higgins, M. S. 1962 Resonant interactions between two trains of gravity waves. J. Fluid Mech. 12, 321–32.Google Scholar
Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12, 333–6.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.Google Scholar
Raetz, G. S. 1959 A new theory of the cause of transition in fluid flows. Norair Rep. No. NOR-59-383.Google Scholar