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On the rippling of small waves: a harmonic nonlinear nearly resonant interaction

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

We show that the rippling often observed on small progressive gravity waves can be explained in terms of a nearly resonant harmonic nonlinear interaction. The resonance condition is that the phase speeds of the two waves must be nearly identical. The in viscid analysis is generalized to any order in a small parameter proportional to the wave steepness. Wave tank measurements provide experimental evidence for most of the predicted results. The phenomenon of resonant rippling is further shown to be not just peculiar to capillary-gravity waves, but in fact possible for any weakly nonlinear dispersive wave system whose dispersion relation has discrete pairs of solutions nearly satisfying the resonance conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 52 , Issue 4 , 25 April 1972 , pp. 725 - 751
Copyright
© 1972 Cambridge University Press

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