Long-term Modelling of Nonlinear High Crests in Narrow-Band Ocean Waves up to the Stokes’ Fifth-order Theory

In this paper, the solution for the return period of a sea storm in which the highest crest exceeds a fixed threshold is considered, by taking into account effects up to the fifth order in a Stokes expansion. By analysing the nonlinear contributions to the long-term modelling of crest heights during a sea storm, it is found that higher order corrections, up to fifth-order, to the linear distributions give crest height slightly smaller than those up to second-order. This result is of interest in engineering applications for the long-term modelling of extreme crest heights.