Directional spreading in surfbeat

Abstract

In the following we consider the forcing of long waves by normally or obliquely incident grouped short waves, also known as surf beat. Two mechanisms responsible for the generation of long waves are considered: the release of the bound long waves associated with changes in the spatial variation of the incident short wave energy [Longuet-Higgins and Stewart, 1964] and the time-varying position of the break point [Symonds et al., 1982]. These mechanisms are examined using near shallow water equations on an alongshore uniform coast, with special attention for the cases of resonant interaction between the incident short waves and edge waves. The effect of directional spreading will be examined in detail. The reason to use linearized equations is twofold. First it renders the possibility to examine the various long wave generation mechanisms separately (without nonlinear interactions complicating the analysis). Second, it provides a quick assessment (computational time is an order of magnitude smaller) of the conditions which are interesting (such as edge waves) and can thus provide the necessary boundary conditions for the more complex nonlinear modelling.