Modelling wind-generated surface gravity waves using similarity in a coupled discrete wave model

Abstract

In deep water, there is a growing observational consensus that supports an ƒ4 variation for the Kitaigorodskii subrange of the high-frequency energy spectra. We therefore re-examine and extend the TMA (Texel Marsen Arsloe) similarity and concepts for shallow water waves, which were originally derived for an ƒ5 Phillips subrange. The similarity for an ƒ4 a subrange is found to closely resemble that of the ƒ5 subrange. The former exists when nonlinear transfer due to wave-wave interactions dominates over other source terms, such as wind input, in the energy balance. Starting with a standard second generation deep water coupled discrete spectral wave model, we implement the TMA similarity. To evaluate our modifications, we perform the real and synthetic shallow water tests of the recent SWIM study. Thus we intercompare our model with HYPAS, an analogously modified deep water coupled hybrid model, and with other wave models which were not based on the TMA similarity. Our model and HYPAS are found to behave quite similarly in the sloping and flat-bottom SWIM tests, compared to the other wave models of the SWIM intercomparison. The more difficult and complex North Sea SWIM hindcast extends this property, in some regards.