Return period of nonlinear high wave crests

Abstract

This paper deals with the long‐term statistics for extreme nonlinear crest heights. First, a new analytical solution for the return period R(η), of a sea storm in which the maximum nonlinear crest height exceeds a fixed threshold η, is obtained by applying the ‘Equivalent Triangular Storm’ model and a second‐order crest height distribution. The probability P(ηc max > η∣[0, L]) that maximum nonlinear crest height in the time span L exceeds a fixed threshold is then derived from R(η) solution, assuming that the occurrence of storms with highest crest larger than η is given by a Poisson process. In the applications, both R(η) and P(ηc max > η∣[0, L]) are calculated for some locations. It is shown that narrowband second‐order approach is slightly conservative, with respect to the more general condition of crest distribution for second‐order three‐dimensional waves. Finally, a comparison with Boccotti, Jasper and Krogstad models is presented.