Wind-wave spectra based on the hypothesis of local equilibrium

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 reexamined to yield the basic validity of the 3/2-power law of Toba orE～? in the range of 0.4≦?≦1, where? is the wave-wind parameter defined by?=ω _p u _*/g; ω _p denotes the peak frequency of the wind-wave spectra,u _* the friction velocity andg the gravitational acceleration. Noticeable deviation is found, however, for?<0.4 or?>1. In particular, the data for large? suggest the existence of an upper limit of the wave nonlinearityE at about 5×10^?2, whereE=Eω _p ⁴ /g² withE the total power of the wind wave spectrum. Then, the spectral form is investigated in detail. As? decreases, 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 ( (tilde omega ) >2.6), the spectrum is found to have a functional form likeu _* ² ω ^?3, which differs from the usualω-dependence asω ^?5 orω ^?4. It suggests weak dependence of the high-frequency spectra on the gravitational accelerationg and on the peak frequencyω _p ; spectral density 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.