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Effects of wave directional spreading and two-peak spectra on the second order wave statistics

Effects of wave directional spreading and two-peak spectra on the second order wave statistics were investigated. Particular attention has been given to the wave crest. Different directional spreading functions for wind-sea and swell have been applied. The results for the Torsethaugen frequency spectrum have been compared with prediction given by the JONSWAP spectrum, the Pierson-Moskwitz spectrum and the 2nd order Forristall crest model. The study shows that for sea states that exhibit a pronounced secondary peak, e.g. due to the presence of swell, the commonly used Forristall crest distribution may be unconservative. Further, for these sea states more severe crest values have been obtained applying the two peaks Torsethaugen spectrum than using the commonly applied JONSWAP spectrum with peak enhancement factor 3.3.

Limitations of the second order wave model to predict extreme crests were investigated. Statistics for freak waves defined according to the criterion c/hs> ê (c=wave crest, hs=significant wave height) was studied. The analyses were based on second order time domain simulations, short-term distributions for crest statistics documented in the literature, and long term field data. Time series of wave elevations have been generated using the Pierson-Moskowitz, JONSWAP and two-peak Torsethaugen frequency spectrum for long-crested seas and deep water. The analysis confirms that wind dominated seas are generally more non-linear than swell dominated seas as they represent steeper sea states, and consequently higher number of freak events are expected in these seas.

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