Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-19T06:25:41.472Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Broer, L. J. F. 1974 Appl. Sci. Res. 30, 430–446.
Chen, B. & Saffman, P. G. 1979 Steady gravity–capillary waves in deep water – I. Weakly nonlinear waves. Stud. Appl. Maths 60, 183–210.Google Scholar
Choi, I. 1977 Contributions a l'étude des mechanismes physiques de la géneration des ondes de capillarité–gravité à une interface air-eau. Thesis, Université d'Aix Marseille.
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Crawford, D. R., Lake, B. M., Saffman, P. G. & Yuen, H. C. 1981 Effects of nonlinearity and spectral bandwidth on the dispersion relation and component phase speeds of surface gravity waves. J. Fluid Mech. 112, 1–32.Google Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.
Favre, A. & Coantic, M. 1974 Activities in the preliminary results of air–sea interaction at IMST. Adv. Geophys. 10A, 291–405.Google Scholar
van Gastel, K., Janssen, P. A. E. M. & Komen, G. J. 1985 On phase velocity and growth rate of wind-induced gravity–capillary waves. J. Fluid Mech. 161, 199–216.Google Scholar
Janssen, P. A. E. M. 1986 The period doubing of gravity–capillary waves. J. Fluid Mech. 172, 531–546.Google Scholar
Kawai, S. 1979 Generation of initial wavelets by instability of a coupled shear flow and their evolution to wind waves. J. Fluid Mech. 93, 661–703.Google Scholar
McGoldrick, L. F. 1972 On the rippling of small waves: a harmonic nonlinear resonant interaction. J. Fluid Mech. 52, 725–751.Google Scholar
Miles, J. W. 1977 On Hamilton's principle for surface waves. J. Fluid Mech. 83, 153–158.Google Scholar
Plant, W. J. & Wright, J. W. 1977 Growth and equilibrium of short gravity waves in a wind-wave tank. J. Fluid Mech. 82, 767–793.Google Scholar
Ramamonjiarisoa, A., Baldy, S. & Choi, I. 1978 Laboratory studies on wind-wave generation, amplification and evolution. In Turbulent Fluxes through the Sea Surface, Wave Dynamics, and Prediction (ed. A. Favre & K. Hasselmann), pp. 403–420. Plenum.
Russel, D. A. & Ott, E. 1981 Chaotic (strange) and periodic behaviour in instability saturation by the oscillation two-stream instability. Phys. Fluids 24, 1976–1988.Google Scholar
Simmons, W. F. 1969 A variational method for weak resonant wave interactions. Proc. R. Soc. Lond. A 309, 551–575.Google Scholar
Valenzuela, G. R. & Laing, M. B. 1972 Nonlinear energy transfer in gravity–capillary wave spectra, with applications. J. Fluid Mech. 54, 507–520.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Tekh. Fiz. 2, 86–94 (Translated in J. Appl. Mech. Tech. Phys. 2, 190–194).Google Scholar