On the distribution of large wave heights: Nonlinear effects

Asymptotic probability models describing large wave heights are reviewed, and the potential effects of nonlinearities due to bound and free waves are explored. It is shown that nonlinearities due to second-order bound waves do not, on average, affect the statistics of large wave heights. This is validated by simulations carried out within the range of validity of the weakly nonlinear second-order theory so as to generate 'realistic' waves whose steepness characteristics do not violate the Stokes limit. Heights of waves representing approximately the largest 1/3 of waves are described quite accurately, in particular, by Boccotti's (Boccotti, 1989) asymptotic distribution. However, waves observed in some oceanic storms and laboratory experiments tend to display higher-order nonlinearities, causing the wave-height statistics to deviate from Boccotti's asymptotic model. Herein, Boccotti's model is generalized so as to include the effects of such nonlinearities approximately. Analyses and comparisons of wave-height distributions estimated from a series of laboratory measurements and four oceanic datasets representing waves observed during severe storms indicate that the generalized model is able to describe large wave heights well and noticeably better than the original Boccotti model.