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On nonlinear interactions in a spectrum of inviscid gravity–capillary surface waves

Published online by Cambridge University Press:  12 April 2006

Dennis Holliday
Dennis Holliday
Affiliation:
R. & D. Associates, P.O. Box 9695, Marina del Rey, California 90291
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Abstract

Using the Fourier components of the velocity potential at the surface in an iterative perturbation theory, the author derives expressions for the modal frequency shifts and modal decay rates in a spectrum of in viscid gravity–capillary surface waves. The expressions differ from those calculated by the perturbation methods of Hasselmann (1962) and Valenzuela & Laing (1972), which are based on expanding the velocity potential about the equilibrium fluid level z = 0. This difference is shown to be due to the failure of the z = 0 perturbation method to converge rapidly enough to produce lowest-order corrections that are smaller than unperturbed quantities. A physical explanation for this failure is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 4 , 21 December 1977 , pp. 737 - 749
Copyright
© 1977 Cambridge University Press

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