Wind-wave Spectra Based on the Hypothesis of Local Equilibrium

Abstract

Wind-wave spectra measured in a wind-flume are analyzed according to the hypothesis of local equilibrium. The gross relation between the wave height and the frequency is reexaminedto yield the basic validity of the 3/2-power law of Toba orE-uin the range of 0.4≤u≤1, where u is the wave-wind parameter defined byu=ω_pu/g;ωpdenotes the peak frequency of the wind-wave spectra, uthe friction velocity andgthe gravitational acceleration. Noticeable deviationis found, however, foru<0.4 oru>1. In particular, the data forlargeusuggest the existence of an upper limit of the wave nonlinearityEat about 5×10^-2, whereE=Eω_p⁴/g²withEthe total power of the wind wave spectrum. Then, the spectralform is investigated in detail. Asudecreases, the normalized spectrum becomes more gradual as a whole, but its forward (low frequency) part tends to show a steeper profile. In the high frequency region (ω>2.6), the spectrum is found to have a functional form likeu²ω^-3, which differs from the usualω-dependence asω-5 orω-4. It suggests weak dependence of the high-frequency spectra on the gravitational accelerationgand on the peak frequencyωp;spectraldensity at high frequencies may be saturated, so that its magnitude may be dominated by the frequencyω, the friction velocityu, the surface tension and the viscosity.