Fig. 6

Composite wave statistics based on wave age of sea states. Top row panels: skewness \(\lambda _3\), excess bound and dynamic kurtosis \(\lambda _{40}^b\) and \(\lambda _{40}^d\) and maximum crest height \(h/H_s\) as a function of wave age \(c_p/U_{10}\) for the Ekofisk ensemble of sea states (squares). Red circles denote sea states whose maximum crest height \(h/H_s>1.4\). Middle and bottom row panels: composite crest and trough exceedance probabilities of the ensembles of developed sea states whose wave age \(c_p/U_{10}>1\) (\(7.0\cdot 10^5\) waves) and that of the youngest sea states whose wave age \(c_p/U_{10}<1\) (\(7.4\cdot 10^5\) waves). Left plot: the contribution of each sea state to the wave statistics is weighted by the values of the Tayfun steepness and wave age. Middle plot depicts the statistics of crest and trough heights of the nonlinear \(\eta\), and the same statistics for the non-skewed free component \(\eta _1\) is depicted in the right plot. Marks denote empirical distributions from data of crest heights (square) and trough heights (circle), R=Rayleigh (dash line), F=3D Forristall (black), TF=\(3^{\textrm{rd}}\) Tayfun-Fedele (red), MNB=Modified-Narrow-Band (green) and NLS¹⁵ (blue) models.