Waves generation and dissipation at the waden sea, Netherlands with Delft3D

Waves modelli g using Delft3D

1. Wave generation and dissipation during storm conditions; an ideal case of the Wadden Sea, Netherlands. Madoche Jean Louis, Dept. of Oceanography & Coastal Sciences College of the Coast & Environment, Louisiana State University, USA. November 30 2022, Baton Rouge, USA

2. Wadden Sea, the study area Ameland inlet Barrier Islands Fig. 1. Bathymetry in the Dutch Wadden Sea relative to local reference height NAP (equivalent to MSL; bathymetry source: Rijkswaterstaat Vaklodingen ), with indicated the islands and tidal inlets in the Dutch Wadden Sea (Roy van Weerdenburg et al. 2021). Fig. 2.  Ameland inlet separated by Terschelling Noordzee and Ameland (Barriers Islands) (Roy van Weerdenburg et al. 2021).

3. Rationale Wind-driven processes Morphological development Water level dynamics Tidal basin connectivity Biology and animal habitats Coastal hydrodynamics (wave + morphology+ hydrodynamic + vegetation dynamics)

4. Research question: How the system respond to external forcings as wind ? How local bathymetry and structure controls waves dynamics ? Table 1. External forcings Fig. 1. External forcings

5. Delft3D Flexible Mesh (FM) model. A 2D depth averaged method developed based on Navier-Stokes Equations (NS). Delft3D FM Suite can simulate storm surges, hurricanes, tsunamis, detailed flows and water levels, waves, sediment transport and morphology, water quality and ecology, and is capable of handling the interactions between these processes The approach for the numerical solution is based on the combination of 2D/3D volume-finite grids D-Waves are based on the third-generation SWAN calculation core.

6. Delft3D Flexible Mesh (FM) model. A 2D depth averaged method developed based on Navier-Stokes Equations (NS). for -β-α< <α-β Modelling of obstacle Energy loss dissipation Where F=h-d is the freeboard above the obstacle(dam) and Hi is the incident significant wave height at the up-wave side of the dam, h is the crest above the dam, d is water level, and are the coefficients based on the shape of the dam (Seelig, 1979).   Whitecapping Where Γ is a steepness-dependent coefficient, k is the wave number, and sigma ˜ and ˜k denote a mean frequency and a mean wave number, respectively (cf. the WAMDI group (1988)). Komen et al. (1984) estimated the value of Γ by closing the energy balance of the waves in fully developed conditions. This implies that this value depends on the wind input formulation that is used. Bottom friction Depth-induced breaking The local rate of change of action density Propagation of action (geographical coordinates) Shift of the relative frequency The depth and current induced refraction Source term in terms of energy density representing the effects of generation, dissipation, and nonlinear wave-wave interactions C bottom is a bottom friction coefficient. E tot and D tot is the rate of dissipation of the total energy due to wave breaking, according to Battjes and Janssen (1978).

7. Grid, bathymetry obstacle (submerged dam Local bathymetry gradient controls wave dynamics properties Obstacle (submerged dam)

8. Waves height Waves heights is correlated to winds input and is limited by bathymetry and breaking conditions

9. Mean wave period Wave period changes because the North sea can partly penetrate the Wadden sea. The new waves generated have shorter wave periods.

10. Wave direction Major dissipation rates appear to be along the barriers landboundary

11. Energy dissipation ? Fig 1. Energy density spectrum from t =1 to t = 6, where t =1 is due to forcings on November 05. Barriers, obstacle act as energy dissipators

12. What about waves direction impact ? Southeast wind Northwest wind

13. What if there is only local wind forcing?

14. And without local wind? Waves heights is correlated to winds input and is limited by bathymetry and breaking conditions

15. Wrap up ! Waves heights is correlated to winds input and is limited by bathymetry and breaking conditions Complex waves interacting field need computational help to be modelled. Forecast wave climate is complex Local bathymetry variability controls wave propagation and dissipation Waves depends both on locals' winds and remote forcing Wave field is sensitive to wind stress, direction, fetch and duration Islands barriers act as energy dissipators. wave energy strongly correlated to the spatial gradient in bathymetry, where bottom friction and depth-induced breaking play a major role in energy dissipation Under typical northerly winds from the North Sea, waves are less impacted by fetch. Still, they are attenuated by the barrier islands and the dam submerged at the entrance of the Ameland inlet directional spreading and wave direction cause strong divergence of wave energy towards the coastline by reducing wave height LIMITATIONS AND UNCERTAINTIES Model is not calibrated nor validated Grid is coarse, limited accuracy Stand alone (not coupled with hydrodynamic nor morphology) Vegetation dynamics not represented Spatial uniformity assumptions for external forcings ALL MODELS ARE WRONG, THEY ARE JUST USEFUL

16. THANK YOU FOR YOUR ATTENTION QUESTIONS (WHICH I DON’T KNOW THE RESPONSE)