The statistics of second-order deep-water random wave trains is investigated through a large and systematic set of numerically generated records. In particular, the properties of extreme crest heights are considered. A previously described numerical synthesisation procedure, based on second-order random wave theory, is applied. Ocean wave elevation records of 4.5 hours duration are generated for a variety of sea states including storm conditions. Each sea state is simulated with 48 independent realisations in order to assure robust statistics. Thus average (expected) values as well as sampling variabilities are worked out. Parameters of the study include skewness and kurtosis values, extreme crest heights as well as the asymmetry of individual extreme waves. Comparisons to available theory are made, verifying that the simulations work satisfactorily. For a 100-year sea state with Hs=15m and Tp=14s an increase of 15% is observed in the expected extreme crest height, relative to the linear case. The corresponding average extreme wave asymmetry factor is increased from 0.50 to 0.58. A considerable sampling variability, with a standard deviation corresponding to about 2m for the extreme crest in this sea state, is also observed.
The nonlinear asymmetry of steep waves on deep water has been previously documented through several studies in the literature. Among other works, we mention here the full scale data analysis by Marthinsen and Winterstein (1992), and Vinje and Haver (1994). Laboratory works on the same matter also exist, such as e.g. nalysis by Stansberg (1991), (1993), and Kriebel and Dawson (1993). In storm sea states, this asymmetry leads to extreme crest heights that can become significantly higher than those predicted by linear theory and Rayleigh distributed peaks. For a 100-year storm, an increase of at least 15% should be expected for the most extreme crest heights. Most of this asymmetry can be explained by second-order nonlinearities in the wave field.
