Large morphological features, so-called sand ridges, with an average height and length in the order of 10 meters and 3 kilometers respectively are located at future offshore wind farm locations in the Dutch North Sea. Recent literature, considering relatively deep water conditions (kh 1, with k the wave number and h the water depth), has shown that a wave field propagating over a shallowing depth transition shows an increase in kurtosis. Kurtosis is a measure for the vertical deviation from the commonly applied linear ocean wave model, and therefore describes a higher probability of occurrence of "rogue" waves. These "rogue" waves are known to the general public from sailors' tales and thrilling videos. Scientifically, rogue waves are described as statistically abnormal waves and are generally classified as waves that exceed twice the significant wave height. Because these waves have an abnormal height, they are associated with extreme forces. Considering the sand ridges at future offshore wind farm locations, and possible increased damages to wind turbines due to rogue waves, this thesis researches if the increased probability of occurrence of rogue waves due to the local bathymetry as observed in the relatively deep water literature also applies to relatively shallow water conditions and the Dutch North Sea. To achieve this objective, physical experiments have been performed in the Hydraulic Engineering laboratory of the Delft University of Technology. Also, an existing statistical model that describes a rogue wave mechanism due to the presence of depth transitions is evaluated. The model describes the rogue wave mechanism as the interaction between the transmitted wave field and second-order components: the free sub- and super-harmonic components generated by the depth transition. As the model assigns a prominent role to these sub- and super-harmonics, it was ensured that these components are generated correctly during the physical experiments. Following, this thesis also assesses and contributes to the second-order wave generation at the TU Delft laboratory facility.

Climate change puts under pressure existing and future coastal interventions. Growing threats like sea-level rise and intensity of storms require solutions to be adaptable and resilient. Nature-based solutions have shown to tackle these challenges while providing social, environmental, and economic benefits. The role of vegetation in coastal protection is increasingly recognized. Aquatic vegetation reduces erosion, storm surge, and incoming wave height.

Large-scale modeling of waves with spectral wave models such as SWAN is indispensable for the design of coastal structures and the assessment of flood risk. Wave dissipation due to vegetation can be modeled in SWAN as increased bottom friction (implicit modeling) or as an additional dissipation function (explicit modeling). The second assumes that vegetation can be represented as rigid cylinders or plates (canopies) with different properties. While some studies concluded that implicit modeling reproduces the spectral evolution of field measurements more closely, others concluded the opposite.

Within the BE-SAFE project, field campaigns measured the spectral energy distribution over salt marshes in the Dutch Wadden Sea during several winter storms. The vegetated foreshore in front of the coastal dike got submerged over 2 m of water during high tide and storm surge. The measurements deployed wave gauges over the study transect, which was defined between the pioneer zone marsh edge and the near-dike location (300 m behind the salt marsh). Calibrating the implicit and explicit models in SWAN brought the modeled total wave energy decay closer to the measurement. Nevertheless, the spectral shape, which describes the energy distribution over frequencies, still showed significant and not yet understood differences near the dike.

A methodology was executed to investigate the mechanisms that could reduce the spectral mismatch between the SWAN wave model and measurements over vegetation. First, the literature highlighted possible mechanisms that could be incorporated for this purpose. Next, a new frequency-distributed explicit dissipation model of Jacobsen et al. (2019) was implemented in SWAN and compared to implicit and explicit models using lab and field measurements.

The results showed that the newly implemented model accurately captures the physics and the change of spectral shapes for all experimentally tested wave conditions and submergences. In contrast, the existing implicit and explicit dissipation models in SWAN reproduce the spectral evolution only under certain circumstances. In the validation and comparison to the field measurements with a much larger water depth than the vegetation height, the model of Jacobsen et al. (2019) correctly captured the vegetation's physical representation and the dissipation on the wind-sea frequencies. Nevertheless, the amount of energy on low frequencies was largely underpredicted by all frequency-distributed models. Therefore, the model of Jacobsen et al. (2019) was modified to include flexibility in a frequency-dependent reduction factor that reproduced the energy decay of the measurements in all frequency regions. Other mechanisms that could be responsible for the mismatch before and over the marsh are the redistribution of energy by non-linear triad interactions, generation of infra-gravity waves, and near-shore currents caused by horizontal variations on the vegetation properties.

The present research provides the range of conditions in which the tested explicit and implicit energy dissipation functions in SWAN are able to simulate the spectral evolution over rigid canopies and flexible salt-marsh vegetation. A new version of SWAN includes a new frequency-distributed explicit model that performed more accurately than existing models for rigid canopies. The physical insights from the research contributed to developing additional versions of SWAN, which performed closely to the energy distribution of the measurements over deeply submerged and flexible salt marsh vegetation species.

References:
Jacobsen, McFall, Van der A (2019). A frequency distributed dissipation model for canopies. Coastal Engineering, 150, 135-146.