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The period-doubling of gravity-capillary waves

Janssen, Peter A. E. M. (1986) The period-doubling of gravity-capillary waves. Journal of Fluid Mechanics, 172 . pp. 531-546. ISSN 0022-1120. doi:10.1017/S0022112086001854.

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In this paper an attempt is made to explain the period-doubling of wind-generated gravity-capillary waves as observed in the experiment of Choi (1977). It is conjectured that period-doubling is closely related to the phenomenon of second-harmonic resonance. In order to obtain a simple dynamical model, results of McGoldrick (1970) and Simmons (1969) are extended to include the effect of wind input and shear in the current. For pure gravity–capillary waves (no wind, no current) the condition for energy transfer from the second harmonic to the fundamental wave of Chen & Saffman (1979) is recovered. We also discuss the effect of wind and we find that wind input gives rise to a very sudden period-doubling. Qualitative agreement with experiment is obtained.

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Additional Information:© 1986 Cambridge University Press. Received 20 June 1985 and in revised form 12 December 1985. Published online: 21 April 2006. The author benefited from discussions with K. van Gastel and G. J. Komen. He is pleased to acknowledge useful discussions with P. G. Saffman and he thanks him for the kind hospitality at Caltech. This work was supported by the Office of Naval Research under Contract N00014-79-C-0412, NR062-639.
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Office of Naval Research (ONR)N00014-79-C-0412
Office of Naval Research (ONR)NR062-639
Record Number:CaltechAUTHORS:20120626-153723971
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Official Citation: Peter A. E. M. Janssen (1986). The period-doubling of gravity–capillary waves. Journal of Fluid Mechanics, 172 , pp 531-546 doi:10.1017/S0022112086001854
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32111
Deposited By: Ruth Sustaita
Deposited On:26 Jun 2012 22:57
Last Modified:09 Nov 2021 21:15

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