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The initial evolution of gravity-capillary waves

Published online by Cambridge University Press:  21 April 2006

Peter A. E. M. Janssen
Peter A. E. M. Janssen
Affiliation:
Department of Oceanography, KNMI, De Bilt, The Netherlands Present address ECMWF, Shinfield Park, Reading, UK.
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Abstract

In this paper we discuss the initial evolution of wind-generated, gravity-capillary waves by means of a dynamical model that includes the effects of wind input, viscous dissipation and three-wave interactions. In particular, we study the generation of the initial wavelets by wind and the subsequent migration of the peak of the spectrum to lower wavenumbers. Under certain conditions a sudden migration of the peak wavenumber is found. It is argued that this sudden migration is related to the phenomenon of second-harmonic resonance. We also observe that during the generation of the initial wavelets by wind, nonlinear three-wave interactions may be important. Therefore, the experimental determination of the growth rate of the waves by wind by just analysing the time series of the surface elevation (as is done by e.g. Kawai 1979 and Plant & Wright 1977) might be in error.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 581 - 597
Copyright
© 1987 Cambridge University Press

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