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

Abstract

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 = (?2)½/?0, with ?2 as the mean-square surface elevation and ?0 as the wavelength corresponding to the waves at the peak of the spectrum. With this parameter, the relationship between ? and ñ is reduced to an identity expressing a pure geometric measure of the sea state, because ?ñ4 = (2πSs)2. By applying the significant slope as a parameter explicitly, we proposed that the traditional empirical formulas relating the nondimensional energy ?, fetch x? and frequency ñ be combined into a single unified relationship as ?ñ/x? = (9/40)Ss9/4. This unified empirical formula governs the wind-wave data equally as well in the field as in the laboratory.