Nonlinear energy transfer in a narrow gravity-wave spectrum

A method is developed for efficient calculation of the rate of energy transfer due to nonlinear resonant interaction in a narrow gravity wave spectrum according to Hasselmann’s theory. The coupling coefficient is perturbed to the first order (in spectral width), and it is shown that for Gaussian spectra the sixfold integral is reduced to a single integration. Comparisons with the limiting case of Longuet-Higgins and Fox show that the effects of the spectral width of a typical narrow wind wave spectrum on the nonlinear energy transfer are very important and cannot be neglected. It is also shown that when these effects are included, the present first order theory is in excellent agreement with large scale numerical computations of Jonswap (Joint North Sea Wave Project) on the forward face of the spectrum. Furthermore, preliminary comparisons with the growth rate of wind-wave spectra measured in Lake Ontario tend to substantiate the Jonswap conclusion that ‘Most of the wave growth on the forward face of the spectrum can be attributed to the nonlinear transfer to longer waves.´