On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model

Abstract

An equation given by Davey & Stewartson (1974) for the evolution of wave packets in three dimensions is employed to discuss the resonant transfer of energy within the peak of a narrow spectrum of gravity waves. It is shown that the coupling coefficient G ( k 1 , k 2 , k 3 , k 4 ) between four nearly equal wavenumbers k 1 ,..., k 4 is not zero (as had been speculated) but is equal to 4π. This implies that the exchange of energy within the peak itself is of dominant importance, and leads to a simplified discussion of the energy transfer.