  Wave impact and run-up onto vertical obstacles are among the most important
phenomena which must be taken into account in the design of coastal structures.
From linear wave theory, we know that the wave amplitude on a vertical wall is
twice the incident wave amplitude with weakly nonlinear theories bringing small
corrections to this result. In this present study, however, we show that
certain simple wave groups may produce much higher run-ups than previously
predicted, with particular incident wave frequencies resulting in run up
heights exceeding the initial wave amplitude by a factor of 5, suggesting that
the notion of the design wave used in coastal structure design may need to be
revisited. 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 extreme wave - coastal structure
interaction.
