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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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