The deep water Wallops frequency spectrum is considered in order to deduce the relevant saturated form, which is able to describe the evolution of the above spectrum in decreasing depth. Numerical simulations are carried out to analyse the behaviour of the saturated form with respect to the spectral form originally defined by Huang et al. Finally, comparisons among different saturated spectral forms are made.
Following the self-similarity shape hypothesis suggested by Kitaigorodskii et al. (1975) for the equilibrium range, Scarsi et al. (1994) deduced the saturated spectral forms in finite depth relevant to different frequency spectra in deep water conditions, like the Pierson-Moskowitz and the mean JONSWAP spectra, which exhibit a -5 power law as the principal frequency dependence, the Donelan and the Battjes spectra, which exhibit a -4 power law for that dependence. Knowledge of the saturated spectral forms is important owing to the fact that they can be usefully employed in easy spectral propagation models, as Bouws et al. (1985) showed with reference to the TMA model. More recently, Gentile et al. (1994) and Rebaudengo Landb et al. (1996, 1999), starting from both a linear approach and a non-linear one, provided a spectral propagation model ADS in decreasing depth, referred to the saturated mean JONSWAP spectrum, which is able to take into account also the other physical processes involved during propagation. Among others, the ADS model, easy to use, has been compared by Gentile (2000) with the well known third generation model named SWAN (Booij et al., 1999), more complex to use, in order to examine, under the same deep water conditions and under the same local depth, the behaviour of both spectral waves and spectral forms. The comparison is very satisfactory, especially with reference to intermediate water depths.
