On the Importance of the Significant Slope in Empirical Wind-Wave Studies

The significant slope of a random wave field is found to be an important parameter in empirical wind-wave studies. This significant slope Ss is defined as Ss = (ζ2)½/λ0, with ζ2 as the mean-square surface elevation and λ0 as the wavelength corresponding to the waves at the peak of the spectrum. With this parameter, the relationship between Ẽ and ñ is reduced to an identity expressing a pure geometric measure of the sea state, because Ẽñ4 = (2πSs)2. By applying the significant slope as a parameter explicitly, we proposed that the traditional empirical formulas relating the nondimensional energy Ẽ, fetch x̃ and frequency ñ be combined into a single unified relationship as Ẽñ/x̃ = (9/40)Ss9/4. This unified empirical formula governs the wind-wave data equally as well in the field as in the laboratory.