Statistical properties of group height and group length in combined sea states

The statistical properties of ocean wave groups are extremely important for the analysis of resonant effects on ships and marine structures. The patterns in combined sea states have attracted increasing attention recently. This study focuses on the probability distributions of the group height and group length as defined by an envelope approach in sea states with bimodal spectra. Wave data from laboratory experiments and numerical simulations are used. The envelope spectra in combined sea states might exhibit a double-peaked structure. Although the bimodal envelope spectrum has slight effect on the group height distribution, the group length might have a multimodal and broader distribution. As a result, the joint distribution might be characterised by a multimodal shape. Further, a mixed Weibull distribution of the marginal distributions of the group parameters and a mixed copula model of their bivariate distributions are constructed. For comparison, a conventional Weibull distribution and a single copula model are also applied to fit the distributions. The results suggest that the single models can be used only to fit the group height distribution. By contrast, the mixed models can provide satisfactory descriptions of both the marginal distributions and joint distributions.