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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 r...

The performance of the spectral wind wave model SWAN in tidal inlet seas was assessed on the basis of extensive wave measurements conducted in the Amelander Zeegat tidal inlet and the Dutch Eastern Wadden Sea, as well as relevant data from other inlets, lakes, estuaries and beaches. We found that the 2006 default SWAN model (version 40.51), the starting point of the investigation, performed reasonably well for measured storm conditions, but three aspects required further attention. First, over the near-horizontal tidal flats, the computed ratio of integral wave height over water depth showed an apparent upper limit using the default depth-limited wave breaking formulation and breaker parameter, resulting in an underprediction of wave heights. This problem has been largely solved using a new breaker formulation. The second aspect concerns wave-current interaction, specifically the wave age effect on waves generated in ambient current, and a proposed enhanced dissipation in negative current gradients. Third, the variance density of lower-frequency wind waves from the North Sea penetrating through the inlets into the Wadden Sea was underpredicted. This was improved by reducing the bottom friction dissipation relative to that of the default model. After a combined calibration, these improvements have resulted in a relative bias reduction in Hm0 from -3% to -1%, in Tm-1,0 from -7% to -3%, and in Tm01 from -6% to -2%, and consistent reductions in scatter, compared to the 2006 default model.

For the calculations of the Hydraulic Boundary Conditions in the framework of the Dutch Legal Flood Safety Assessment (WTI), wave statistics obtained at deeper water buoys need to be transformed to the toe of the dike using the wave action model SWAN. This transformation is particularly challenging in complex tidal inlet systems such as the Wadden Sea and the Western Scheldt in the Netherlands. Although various model improvements have been made in SWAN, particularly in the propagation and bottom friction dissipation, one of the unresolved issues is that the penetration of North Sea swell waves into the tidal inlets is still underestimated by SWAN. The goal of this study is to verify the hypothesis that nonlinear interactions, in particular the sub-harmonic triad interactions, play a major role in the transmission of energy from flats into the channel, and that this process can explain SWAN’s under-prediction of wave energy penetration. Since SWAN or any other wave-action equation type models lacks the relevant physics to study this problem, the Boussinesq-type TRITON model is used as well to verify the hypothesis. The conceptual idea, raised by Toledo (2013), is that sub-harmonic wave interactions between second harmonic and basic components generate a wave component of the same frequency as the primary component but at a wider angle of approach. As a consequence, the energy density spectra become directionally broader. From a series of idealized cases with monochromatic and bi-chromatic waves propagating up and down a slope we conclude that the TRITON model results confirm the conceptual idea of 2D nonlinear interactions. Both sub-harmonic wave interactions (to lower frequencies) and super-harmonic wave interactions (to higher frequencies) prove to be important. These insights can be applied to the situation with waves propagating on a tidal flat towards a channel. In case the basic components approach the channel under a sharp angle, such that they will not be able to enter the channel due to refraction, the sub-harmonic components could approach the channel under a less sharp angle and enter the channel. In our study a clear difference between the TRITON and SWAN energy density spectra in and across the channel is observed, as the 2D nonlinear interactions cannot be modeled with the co-linear 1D approach in SWAN. The hypothesis that nonlinear interactions play a major role in the transmission of energy from flats into the channel is confirmed, at least for the cases considered in this study. Additional investigations are still required in order to quantify and generalize the effect of nonlinear interactions on this transmission of energy. In addition, it is recommended to extend the presently implemented three-wave interaction formulation in SWAN to account for directional super- and sub-harmonic interactions.

Over the last five years a research program has been carried out to assess the performance of the spectral wave model SWAN in the Wadden Sea so that it may be used for the transformation of offshore wave conditions to wave boundary conditions near the sea defenses (dikes and dunes). The assessment was done on the basis of extensive wave measurements conducted in Ameland inlet and the Dutch Eastern Wadden Sea, as well as relevant data from lakes and estuaries. After a first round of assessment, we found that SWAN performed reasonably well for storm conditions but three aspects required further attention. Firstly, focusing on the main channel, SWAN formulations needed to be modified in order to eliminate overprediction of the significant wave height in opposing currents. Secondly, the primary spectral peak of North Sea waves penetrating into the inlet was underpredicted. Best results were obtained when the refraction of low-frequency waves was limited and the bottom friction coefficient was set at a lower value than the current default for wind seas. Thirdly, over the tidal flats the computed ratio of integral wave height over water depth showed an apparent upper limit using the conventional Battjes and Janssen (1978) depth-limited wave breaking formulation, because the wave growth over finite depth is hampered by the present formulation of depth-induced wave breaking. The problem has been solved using a new breaker formulation. All these improvements have lead to a wave transformation model with which reliable wave conditions in the Wadden Sea and related complex areas can be determined.