A general theory of three-dimensional wave groups Part II: Interaction with a breakwater

Abstract

The equation obtained in Part I predicts how an exceptionally high wave occurs at any fixed point x o within a wind wave field. The equation may be applied with a theoretical spectrum or directly with the random time series obtained by an array of wave gauges in the field. From both approaches, it emerges that a very high wave at a breakwater occurs because a well-defined three-dimensional wave group at the apex of its development hits against the breakwater, and that a very high wave at some distance before the breakwater occurs because of the collision of two wave groups: the first one going back after having been reflected, and the second one approaching the breakwater. In order to test the theory, a special breakwater was assembled off the beach at Reggio-Calabria where the significant height of the wind waves typically ranges from 0.20 to 0.40 m. When an exceptionally high wave ( H = 9.6 σ) occurred at a point before this breakwater, the records made by a gauge array confirmed all the essential features of the prediction.