Statistical properties of group energy and group duration for unidirectional ocean wave groups

Abstract

The statistical properties of ocean wave groups play an important role in determining the design of marine structures and in analyzing of hydrodynamic phenomena. Unlike the definition of wave groups based on continuous large waves under the assumption of a narrow band in previous studies, the paper investigates the characteristics of all unidirectional wave groups that may lead to responses of structures in not only narrow but also wide spectra. Both marginal and joint distributions of group energy and duration for wave groups with various peak periods and spectral widths are analyzed. It is found that Generalized Extreme Value (GEV) distributions can provide excellent fits for both the marginal probability distributions of group energy and group duration. Moreover, a Gaussian Copula function can best fit the joint distribution of group energy and group duration. Last, formulae to predict the univariate and bivariate possibility distributions of group energy and group duration are constructed by giving a peak period and a spectral width of a sea state. After testing numerous wave cases, it is found that the formulations predict statistical properties of wave groups accurately in both narrow and wide spectral width as a peak period varying from 6.0 to 17.0 s.