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On Wilton's ripples: a special case of resonant interactions

Published online by Cambridge University Press:  29 March 2006

L. F. McGoldrick
L. F. McGoldrick
Affiliation:
Department of the Geophysical Sciences, The University of Chicago
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Abstract

The phenomenon of second harmonic resonance for capillary-gravity waves is reconsidered here by the asymptotic method of multiple time and space scales. The periodic finite amplitude waves of permanent form found by Wilton in 1915 which correspond to this configuration are shown to be no more than a special case of the more general resonant interaction theory, and owe their existence to a critical choice of initial conditions. It is further suggested that the influence of viscous dissipation will render this solution virtually undetectable in a real liquid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 193 - 200
Copyright
© 1970 Cambridge University Press

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References

Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Waltham, Mass.: Blaisdell-Ginn.
Mcgoldrick, L. F. 1965 Resonant interactions among capillary-gravity waves. J. Fluid Mech. 21, 305–331.Google Scholar
Mcgoldrick, L. F. 1970 An experiment on capillary-gravity resonant wave interactions. J. Fluid Mech. 40, 251–271.Google Scholar
Pierson, W. J. & Fife, P. 1961 Some non-linear properties of long-crested periodic waves with lengths near 244 centimetres. J. Geophys. Res. 66, 163–179.Google Scholar
Simmons, W. F. 1969 A variational method for weak resonant wave interactions. Proc. Roy. Soc. A 309, 551–579.Google Scholar
Wilton, J. R. 1915 On ripples. Phil. Mag. (6) 29, 688–700.Google Scholar