Non linear highest sea wave groups in an undisturbed field and in front of a vertical wall

Abstract

In this paper some non-linear effects for the mechanics of sea wave groups with large waves are investigated, either for waves in an undisturbed field or for waves in front of a vertical wall. To the first-order in a Stokes expansion, Boccotti s quasi-determinism theory enables us to foresee the mechanics of wave groups, either in undisturbed or in diffracted fields, when a large wave occurs. The first formulation of this theory shows the random group mechanics when a large crest height occurs (New wave); the second theory formulation gives the random group mechanics when a large crest-to-trough wave height occurs. The quasi-determinism theory in both formulations, for undisturbed fields, was extended recently to the second-order by the author. In this paper the procedure to derive the second-order solution is analyzed and is applied to random wave groups in front of a vertical wall. The non-linear effects are then investigated in space-time domain, and it is obtained a good agreement of analytical predictions with both field data and data from numerical simulation.