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Measurements of third-order resonant wave interactions

Published online by Cambridge University Press:  28 March 2006

L. F. Mcgoldrick ,
O. M. Phillips ,
N. E. Huang  and
T. H. Hodgson
L. F. Mcgoldrick
Affiliation:
The Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland Present address: The Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois.
O. M. Phillips
Affiliation:
The Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
N. E. Huang
Affiliation:
The Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland
T. H. Hodgson
Affiliation:
The Department of Mechanics, The Johns Hopkins University, Baltimore, Maryland Present Address: Department of Aerodynamics, The College of Aeronautics, Cran-field, England.
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Abstract

This paper presents the results of experiments on the resonant interaction of gravity waves. Two mutually-orthogonal primary wave trains are generated in a tank and their interaction products studied at various positions on the surface. Under suitable conditions, the growing resonant third-order interaction product is identified; its amplitude is shown to be a linear function of the interaction distance. The band-width of the response decreases with increasing distance, as is characteristic of the phenomenon of resonance. The ratio of the frequencies of the primary waves at resonance is very close to that predicted theoretically; the growth rate of the third component is close to, though about 20% higher than, the predicted value. Conditions far from resonance are also studied; it is found that the growing tertiary wave is absent in this case.

These results offer the first unambiguous experimental demonstration of resonant wave interactions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 3 , July 1966 , pp. 437 - 456
Copyright
© 1966 Cambridge University Press

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References

Ball, F. K. 1964 Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465–78.Google Scholar
Benney, D. J. 1962 Non-linear gravity wave interactions. J. Fluid Mech. 14, 577–84.Google Scholar
Bretherton, F. P. 1964 Resonant interaction between waves, the case of discrete oscillations. J. Fluid Mech. 20, 457–79.Google Scholar
Hasselman, K. 1962 On the non-linear energy transfer in a gravity wave spectrum. Part 1. General theory J. Fluid Mech. 12, 481–500.Google Scholar
Hasselman, K. 1963a On the non-linear energy transfer in a gravity wave spectrum. Part 2. Conservation theorems; wave-particle analogy; irreversibility. J. Fluid Mech. 15, 273–81.Google Scholar
Hasselman, K. 1963b On the non-linear energy transfer in a gravity wave spectrum. Part 3. Evaluation of the energy flux and sea-swell interaction for a Newmann spectrum. J. Fluid Mech. 15, 385–98.Google Scholar
Huber, E. A. 1958 Improved system for the measurement of heights of water waves. Report no. 1–78 Control Systems Laboratory. University of Illinois, Urbana, Illinois.Google Scholar
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, 333–36.Google Scholar
Longuet-Higgins, M. S. & Smith, N. D. 1966 An experiment on third-order resonant wave interactions. J. Fluid Mech. 25, 417.Google Scholar
Mcgoldrick, L. F. 1965 Resonant interactions among capillary-gravity waves. J. Fluid Mech. 21, 305–31.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
Pierson, W. J. 1961 Comments on a paper by O. M. Phillips, appearing in Proceedings of a Conference on Ocean Wave Spectra, Easton, Md., 1961. Published as Ocean Wave Spectra, pp. 180–6 and 187–8. Prentice-Hall, Inc., Englewood Cliffs, N.J. (1963).Google Scholar
Thorpe, S. A. 1966 On wave interactions in a stratified fluid. J. Fluid Mech. 24, 737.Google Scholar