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The period-doubling of gravity–capillary waves

Published online by Cambridge University Press:  21 April 2006

Peter A. E. M. Janssen
Peter A. E. M. Janssen
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA Permanent address: KNMI, De Bilt, Holland.
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 172 , November 1986 , pp. 531 - 546
Copyright
© 1991 Cambridge University Press

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