Three-dimensional nonlinear standing wave groups: formal derivation and experimental verification

An analytical non-linear theory is presented for the interaction between three-dimensional sea wave groups and a seawall during an exceptionally high crest or deep trough in the water elevation. The solution to the second-order of the free-surface displacement and the velocity potential is derived by considering an irrotational, inviscid, incompressible flow bounded by a horizontal seabed and a vertical impermeable seawall. From this, an analytical expression for the non-linear wave pressure is obtained. The resulting theory can fully describe the mechanics at the seawall and in front of it, which are represented by a strongly inhomogeneous wave field, and demonstrate that it is influenced by characteristic parameters and wave conditions. The theoretical results are in good agreement with measurements conducted during a small-scale field experiment at the Natural Ocean Engineering Laboratory in Reggio Calabria (Italy). Comparisons of the theoretical and experimental results show that some distinctive phenomena involving the wave pressures of very high standing wave groups at a seawall, in the absence of either overturning or breaking waves, may be associated with non-linear effects.