Extreme wave run-up on a vertical cliff

Wave impact and run-up onto vertical obstacles constitutes one of the main phenomena which have to be taken into account in the design of coastal structures. From the linear wave theory we know that the wave height on a vertical wall is twice the incident wave amplitude. Weakly nonlinear theories bring some small corrections to this result. However, in the present study we show that certain simple wave groups may produce much higher run-ups ever predicted by previous theoretical investigations. Consequently, the results presented in this study can be considered as a note of caution for practitioners, on one side, and as a challenging novel material for theoreticians who work in the field of the wave/structure interaction.