Mechanics of nonlinear random wave groups interacting with a vertical wall

Nonlinear random wave groups interacting with a vertical wall are investigated. The analytical solution for the second-order free surface displacement and velocity potential when a high crest occurs at some fixed point on, or close to, the vertical wall is obtained. The solution is exact for any water depth, and it is given as a function of the frequency spectrum of the incident waves. It is obtained that the effects of nonlinearity strongly modify the linear structure of wave groups both in the space and the time domain. The maximum effect of nonlinearity occurs when the high wave hits the wall. Furthermore, it is shown that in finite water depth, the nonlinearity increases as the bottom depth decreases. Finally, a validation by means of Monte Carlo simulations of nonlinear random waves in reflection is given.