The Role of Nonlinear Momentum Fluxes on the Evolution of Directional Wind-Wave Spectra

Abstract

t has long been known that nonlinear wave?wave interactions produce stationary solutions related to constant energy flux through the equilibrium range when a deep-water spectrum follows an f?4 form, as has been verified in numerical studies in which spectra follow a constant angular spreading distribution. This paper shows that, although energy fluxes through such spectra remain essentially constant, momentum fluxes do not. On the other hand, if the angular distribution of a spectrum is allowed to behave in a manner consistent with observations, both the energy flux and the momentum flux tend to remain constant through a major portion of the spectrum. Thus, it appears that directional distributions of energy within wind-wave spectra adjust to a form consistent with nondivergent nonlinear fluxes, suggesting that these fluxes likely play a very prominent role in the evolution of directional spectra during wave generation.