Some evidence on the effect of nonlinearity on the position of the equilibrium range in wind-wave spectra

1964 ◽  
Vol 11 (2) ◽  
pp. 321
Keyword(s):  
Wind Wave ◽  
Wave Spectra ◽  
Equilibrium Range

Breaking waves and the equilibrium range of wind-wave spectra

1997 ◽  
Vol 342 ◽  
pp. 377-401 ◽  
Author(s):  
S. E. BELCHER ◽  
J. C. VASSILICOS
Keyword(s):  
High Frequency ◽  
Wind Wave ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Wave Spectra ◽  
Scale Invariant ◽  
Self Similar ◽  
Dynamical Properties ◽  
Dynamical Balance ◽  
Equilibrium Range

When scaled properly, the high-wavenumber and high-frequency parts of wind-wave spectra collapse onto universal curves. This collapse has been attributed to a dynamical balance and so these parts of the spectra have been called the equilibrium range. We develop a model for this equilibrium range based on kinematical and dynamical properties of breaking waves. Data suggest that breaking waves have high curvature at their crests, and they are modelled here as waves with discontinuous slope at their crests. Spectra are then dominated by these singularities in slope. The equilibrium range is assumed to be scale invariant, meaning that there is no privileged lengthscale. This assumption implies that: (i) the sharp-crested breaking waves have self-similar shapes, so that large breaking waves are magnified copies of the smaller breaking waves; and (ii) statistical properties of breaking waves, such as the average total length of breaking-wave fronts of a given scale, vary with the scale of the breaking waves as a power law, parameterized here with exponent D.

The equilibrium range of wind wave spectra: an explanation based on white noise

2007 ◽  
Vol 6 (4) ◽  
pp. 345-348 ◽  
Author(s):  
Dejun Dai ◽  
Wei Wang ◽  
Fangli Qiao ◽  
Yeli Yuan
Keyword(s):  
White Noise ◽  
Wind Wave ◽  
Wave Spectra ◽  
Equilibrium Range

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

2011 ◽  
Vol 41 (4) ◽  
pp. 781-801 ◽  
Author(s):  
Donald T. Resio ◽  
Charles E. Long ◽  
William Perrie
Keyword(s):  
Energy Flux ◽  
Wind Wave ◽  
Stationary Solutions ◽  
Wave Spectra ◽  
Wave Interactions ◽  
Numerical Studies ◽  
Momentum Fluxes ◽  
Directional Distributions ◽  
Equilibrium Range

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.

Sign in / Sign up

Export Citation Format

Share Document