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

Donald T. ResioU.S. Army Engineer Research and Development Center, Vicksburg, Mississippi

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Charles E. LongU.S. Army Engineer Research and Development Center, Vicksburg, Mississippi

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William PerrieFisheries and Oceans Canada, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada

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Abstract

It 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.

Corresponding author address: Donald. T. Resio, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180. E-mail: donald.t.resio@usace.army.mil

Abstract

It 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.

Corresponding author address: Donald. T. Resio, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180. E-mail: donald.t.resio@usace.army.mil
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