Generalized Boccotti distribution for nonlinear wave heights

• We consider effects of third-order nonlinearities on wave-height distributions.
• Such effects are of importance in narrowband waves or unsteady sea states.
• We generalize Boccotti's distribution to include third-order effects, approximately.
• We compare generalized and original Boccotti distributions with oceanic and lab data.
• Generalized distribution provides noticeably improved predictions of observed data.

Nonlinearities due to second-order bound waves do not, on average, affect the statistics of large wave heights. Heights of waves representing approximately the largest 1/3 of waves are described quite accurately, in particular, by Boccotti's asymptotic distribution (Boccotti, 1989). However, waves observed in some oceanic storms and laboratory experiments tend to display higher-order nonlinearities, causing the statistics of wave heights to deviate from the predictions of the Boccotti distribution. Herein, this distribution is modified and generalized so as to include the effects of such nonlinearities approximately. Analyses and comparisons of wave-height distributions estimated from two oceanic datasets representing waves observed during severe storms and a series of laboratory measurements suggest that the generalized model describes large wave heights well and noticeably better than the original Boccotti distribution and other models proposed for describing wave heights affected by third-order nonlinearities.