Journal of Fluid Mechanics

The period-doubling of gravity–capillary waves

Peter A. E. M.  Janssen a1p1
a1 Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

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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.

(Published Online April 21 2006)
(Received June 20 1985)
(Revised December 12 1985)

p1 Permanent address: KNMI, De Bilt, Holland.