SECOND-ORDER CREST STATISTICS OF REALISTIC SEA STATES

Current engineering design employs second-order irregular wave theory to predict extreme crest elevations (Forristall, 2000). However, there are several field measurements of waves with crest elevations significantly larger than those predicted at second-order; the New Year Wave at the Draupner East platform being one such example (Haver and Anderson, 2000). Consequently, several authors have sought explanations for the occurrence of these so-called freak, rogue or abnormal waves. These explanations include crossing-seas (Donelan and Magnusson, 2005) and higher-order unidirectional effects (Baldock et al., 1996; Gibson and Swan, 2007). Considering the second-order distribution (Forristall, 2000), there are two distinct shortcomings. First, the crest statistics are based on second-order, time-domain simulations that employ the JONSWAP spectrum and therefore are only strictly applicable for unimodal JONSWAP spectra. Evidence of this is given by BitnerGregersen and Hagen (2003) who have found discrepancies between Forristall’s distribution in bimodal sea states. Second, it neglects nonlinear effects that occur beyond second-order. These higher-order effects have been demonstrated by (Gibson and Swan, 2007) who found local and rapid energy shifts occurring in the vicinity of an extreme event on account of third-order resonant interactions. These energy shifts are dependent on both the frequency bandwidth and the directional spreading of the underlying spectrum. The first shortcoming can be overcome by employing the Spectral Response Surface (SRS) method (Tromans and Vanderschuren, 2004), which has no restriction on spectral shape and has been applied to combined windsea and swell sea states by Tromans et al. (2007). The second shortcoming has been resolved by Gibson et al. (2007) who coupled the SRS method with the fully nonlinear Fourier-based model of Bateman et al. (2001). However, so far this has only been achieved for unidirectional seas. Therefore, as realistic sea states are directional, it is necessary to revert to the SRS with second-order wave theory and build on the work of Tromans et al. (2007). This paper will add to the literature by employing the SRS method to investigate various bi-modal sea-states. These sea states will combine various fetch-limited wind-seas described by the JONSWAP spectrum . Some