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Numerical calculations of steady gravity-capillary waves using an integro-differential formulation

Published online by Cambridge University Press:  19 April 2006

James W. Rottman and
D. B. Olfe
James W. Rottman
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, California 92093
D. B. Olfe
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, California 92093
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Abstract

A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 4 , 29 October 1979, pp. 777 - 793
Copyright
© 1979 Cambridge University Press

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