# Nonlinear Energy Transfer between Random Gravity Waves

## Abstract

A computational scheme for calculating transfer functions is applied to a few typical spectra. The results clarify the change of the transfer function with the increase in the spectral sharpness. That is, they show how the transfer function obtained by Webb for a broad spectrum of Pierson-Moskowitz on the basis of Hasselmann’s model changes into those by Fox or Dungey and Hui for the narrow spectra of jonswap on the basis of Longuet-Higgins’s model or its improved version. Furthermore, an example is presented which shows that for a spectrum expressed as a sum of two spectra with peak frequencies and peak spectral densities different from each other, energy flows so as to smooth out the spectral peak at the higher frequency much more intensely than expected from a simple superposition. The basic features of transfer functions thus obtained are explained well from the two properties: (1) that for most cases of resonant four waves, energy flows from the pair of intermediate frequencies toward the pair of outer (higher or lower) frequencies and (2) that the coupling coefficient depends strongly on the mean frequency of the resonant four waves and the configuration of their wavenumber vectors.

## Keywords

Transfer Function Energy Flow Coupling Coefficient Wind Wave Action Density## Preview

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## References

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