Journal of Fluid Mechanics

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

K.  Hasselmann a1
a1 Institute for Naval Architecture, University of Hamburg

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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.

(Published Online March 28 2006)
(Received August 18 1961)

p1 Present address : Institute of Geophysics and Planetary Physics, University of California, La Jolla.