On the Reflection of Non-Linear Random Wave Groups with High Crests

In this paper, the analytical second-order solution for the reflection of 2-D random wave groups with a very high crest is obtained, by considering the boundary value problem of an irrotational flow with a free surface and by applying the ‘Quasi-Determinism’ theory. The non-linear random processes free surface displacement, velocity potential and wave pressure, when a large wave crest occurs at a fixed point on, or close to, a vertical wall are derived. They are given as a function of the frequency spectrum of incident waves. Finally, the wave force on the wall is obtained when either the extreme crest or the corresponding deepest wave trough occur on the wall. It is shown that, by considering second-order wave pressures, the wave force given by wave trough (in absolute value) may be greater than the wave force produced by the wave crest, in agreement with experimental data.