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

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  • 1 NASA Wallops Flight Center, Wallops Island, VA 23337
  • | 2 Oceanic Hydrodynamics, Inc., Salisbury, MD 21801
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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 = (ζ2)½0, 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 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 , fetch and frequency ñ be combined into a single unified relationship as Ẽñ/ = (9/40)Ss9/4. This unified empirical formula governs the wind-wave data equally as well in the field as in the laboratory.

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 = (ζ2)½0, 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 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 , fetch and frequency ñ be combined into a single unified relationship as Ẽñ/ = (9/40)Ss9/4. This unified empirical formula governs the wind-wave data equally as well in the field as in the laboratory.

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