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On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory

Published online by Cambridge University Press:  28 March 2006

K. Hasselmann
K. Hasselmann
Affiliation:
Institute for Naval Architecture, University of Hamburg
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Abstract

The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 4 , April 1962 , pp. 481 - 500
Copyright
© 1962 Cambridge University Press

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References

Hasselmann, K. 1960 Schiffstechnik, 7, 191–5.
Hasselmann, K. 1961 Proc. Conf. Ocean Wave Spectra, Easton, Md. (to be published).
Longuet-Higgins, M. S. 1962 J. Fluid Mech. 12, 321.
Longuet-Higgins, M. S. & Phillips, O. M. 1962 J. Fluid Mech. 12, 321.
Munk, W. H. 1961 Proc. Conf. Ocean Wave Spectra, Easton, Md. (to be published).
Phillips, O. M. 1957 J. Fluid Mech. 2, 417–45.
Phillips, O. M. 1960 J. Fluid Mech. 9, 193–217.
Tick, L. J. 1958 N. Y. Univ. Coll. Eng. Sci. Paper No. 11.