Parameters in wind-wave frequency spectra and their bearings on spectrum forms and growth

The spectrum variance m₀, peak frequency ω₀ and peakness factor p are expressed in terms of nondimensional fetch and duration by making use of relations which are derived through comparing and analyzing existing empirical formulas for the growth of significant wave height and period. The main features of spectrum growth as specified by these parameters agree with those of the JONS-WAP experiments. For given wind speed and fetch, the high frequency parts beyond the peaks of shallow water spectra almost coincide with that of the corresponding deep water spectrum, whereas the low frequency parts differ appreciably. The method developed in this paper predicts smaller significant wave height as well as smaller wave period for shallow water spectra in contrast to the theoretical result of Kitaigorodskii et al, in which the peak frequency, and consequently the significant wave period, remains basically unchanged for different water depths. Spectra are further reduced to a form in which only significant wave height as well as smaller wave period for shallow water spectra in contrast to the theoretical result of Kitaigorodskii et al., in which the peak frequency, and consequently the significant wave period, remains basically unchanged for different water depths. Spectra are further reduced to a form in which only significant wave height and period are left as parameters, the peakness factor being replaced by the wave steepness through an empirical relation between them. Spectra in this form have been verified by observations.