The present work presents physical laboratory measurements of surface elevation and pore water pressures in a fine sand bed under bichromatic waves in a large-scale laboratory experiment. This was done at three cross-shore locations in the swash zone, with pressures being measured at different depths in the bed. The measurements show that the pore pressure signal decays and shifts with increased depth. These measurements are used to validate a practical model, based on the theory of Yamamoto et al. (1978, https://doi.org/10.1017/S0022112078003006) and Guest and Hay (2017, https://doi.org/10.1002/2016JC012257). The model corresponds well with the measurements (nRMSE < 0.2 and R² > 0.95 for most probes) and shows that a frequency-based model can reproduce the pressures in the bed, despite the bed being exposed during dry periods. Furthermore, the model provides the opportunity to calculate pressure gradients, both throughout the bed and at the bed surface. These modeled pressure gradients at the bed surface show that the vertical pressure gradient can have an important impact on the Shields parameter, thereby influencing sediment transport.

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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.

Floating offshore wind platforms may be subjected to severe sea states, which include both steep and long waves. The hydrodynamic models used in the offshore industry are typically based on potential-flow theory, and/or Morison's equation. These methods are computationally efficient, and can be applied in global dynamic analysis considering wind loads and mooring system dynamics. However, they may not capture important nonlinearities in extreme situations. The present work compares a fully nonlinear wave tank (NWT), based on the viscous Navier-Stokes equations, and a second-order potential-flow model for such situations. A validation of the NWT is first completed for a moored vertical floating cylinder. The OC5-semisubmersible floating platform is then modelled numerically both in this nonlinear NWT and using a second-order potential-flow based solver. To validate both models, they are subjected to non-steep waves and the response in heave and pitch is compared to experimental data. More extreme conditions are examined with both models. Their comparison shows that if the structure is excited at its heave natural frequency, the dependence of the response in heave on the wave height and the viscous effects cannot be captured by the adjusted potential-flow based model. However, closer to the inertia-dominated region, the two models yield similar responses in pitch and heave.

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