Wave propagation into complex coastal systems and the role of nonlinear interactions

The phase-averaged wave model Simulating WAves Nearshore (SWAN) is often used for the design of dikes and harbors. However, various hindcast studies have shown that SWAN underpredicts the wave energy when waves are penetrating into bathymetries with shallow areas traversed by channels, such as tidal inlets or harbor entrances. The underprediction of these waves could lead to dike failure or shipping downtime as a consequence of incorrect hydraulic loads. This paper presents an explanation for the underprediction of this wave penetration. By comparing a series of SWAN computations with laboratory measurements and computations with the Boussinesq-type wave model TRITON, it is demonstrated that the absence of various subharmonic and superharmonic interactions in SWAN causes an unrealistic amount of energy to be trapped on the channel slopes owing to wave refraction. The two-dimensional nonlinear interactions, which appear to be present in the measurements and TRITON results, broaden the directional range of the energy density spectrum when waves propagate over a sloping bottom. Owing to the directional broadening of the spectrum, more energy exists at angles smaller than the frequency-dependent critical angle for refraction, and therefore more wave energy is transmitted into and across channels, especially when waves approach the channel under an angle. It is recommended that this insight be used to find an alternative formulation for the present one-dimensional threewave interaction formulation in SWAN.