Danish waters hydrodynamic model

DHI’s Danish waters hydrodynamic model (HDDKW) provides information on water levels and depth-averaged currents established through numerical modelling using the MIKE 21 Flow Model FM [17]. The general settings of HDDKW are summarised in Table 2.6.

The MIKE 21 Flow Model is based on the numerical solution of the two-dimensional (2D) incompressible Reynolds-averaged Navier-Stokes (RANS) equations, subject to the assumptions of Boussinesq and hydrostatic pressure.

The model is applicable for the simulation of hydraulic and environmental phenomena in lakes, estuaries, bays, coastal areas, and seas where

stratification is negligible. The model can be used to simulate a wide range of hydraulic and related items, including tidal exchange, currents, and storm surges.

The HDDKW model domain includes all Danish nearshore waters, plus areas offshore of Norway, Sweden, Poland, Germany, and the Netherlands (Figure 2.10). The model domain covers a total area of approximately 220,0000 km² and has three open (‘sea’) boundaries: 1) an eastern boundary in the Baltic Sea between Poland and Sweden, 2) a western boundary in the North Sea between Norway and the Frisian Islands (Netherlands), and 3) a short boundary from the Frisian Islands to the mainland of the Netherlands.

HDDKW is based on an unstructured flexible mesh with refined resolution in shallow areas. The resolution of the model is 3 to 4 km in offshore areas, decreasing to around 2 km in Danish nearshore waters. Near to the Danish coastline, the resolution varies from 1 km to around 500 m. At the Hesselø offshore wind farm site, the resolution of the HDDKW mesh is around 2 km (see left-hand panel of Figure 2.11.). Bathymetry data in the Kattegat was provided from the EMODnet DTM (see Section 2.1.2 of this report, as well as Section 2.1 of [12]).

The Danish waters hydrodynamic model is forced across its open (sea) boundaries by spatially and temporally varying water levels and

depth-averaged currents extracted from DHI’s regional North Europe Hydrodynamic model (HDNE). These open boundaries include the effects of both tide and surge (see Section 3.2 of [12] for further details). HDDKW also includes locally generated surge driven by the wind and air pressure fields from the CREA6 atmospheric model (see Section 2.3.1).

The HDDKW model also includes tidal potential, i.e., forcing directly generated by the variations in gravity due to the relative motion of the earth, the moon, and the sun. The forcing acts through-out the computational domain, calculated as the sum of 11 harmonic terms, each representing a specific constituent (see Section 4.6 of [17]).

Calibration and validation of HDDKW has been performed based on eight water level stations in the model domain: seven stations in Denmark and one in Norway (see Section 3.5 and 3.6 of [12]). Further validation of modelled water levels for stations in the area around the Hesselø OWF is presented in Section 3.3.1 of this report. An additional assessment of depth-averaged currents is also included in Section 3.3.2.

The outputs from HDDKW include water level relative to mean-sea-level (WL), depth-averaged current speed (CS), and depth-averaged current direction (CD), which are saved for each model mesh element at an output time interval of 0.5-hours.

Page 23 Table 2.6 General settings of DHI’s Danish Waters hydrodynamic model (HDDKW)

Setting HDDKW

Simulation period 1995-01-01 to 2018-12-31 (24 years)

Basic equations 2D incompressible Reynolds averaged Navier-Stokes (RANS) equations

Horizontal mesh

Variable resolution unstructured grid, 3 – 4 km in offshore areas, 2 km in Danish waters (including area around the Hesselø OWF development area), and 1 km to 500 m at Danish Coastline (see Figure 2.10 and Figure 2.11)

Density Barotropic

Model time step (adaptive) 0.01 to 300 seconds Model output time interval 0.5 hours

Atmospheric forcing Wind and air pressure from the CREA6 atmospheric model (see Section 2.3.1) Tidal potential 11 constitutes (see Section 4.6 of [17])

Boundary conditions Spatially and temporally varying water levels (tide + surge) extracted from DHI’s North Europe hydrodynamic model (HDNE)

Output parameters

• Water level relative to mean sea level (WL)

• Depth-averaged current speed (CS)

• Depth-averaged current direction (CD) The hydrodynamic setting of the Kattegat

The Hesselø OWF is located within the Kattegat, the major hydrographic transition zone between the brackish waters of the Baltic Sea (to the South) and the saline waters of the North Sea (to the North, via the Skagerrak). The waters of the Kattegat are generally described as two-layered consisting of:

• The northwards flow of the low salinity Baltic Current at the surface, with seasonally varying salinity and temperature

• An underlying counter-current of oceanic waters from North Sea

The density gradients between the different water masses plays an important role in setting the circulation in the Kattegat. Strong wind-generated flows also modify the conditions over relatively short time periods. These 3-dimensional phenomena will not be replicated by a 2-dimensional hydrodynamic model such as HDDKW, which is suited to describing barotropic flows where stratification is negligible.

If the currents and a possible stratification are critical for structural design, an analysis based on a three-dimensional hydrodynamic model should be considered. Such an analysis is not part of the scope of work for this site metocean conditions assessment

Figure 2.10 Domain and mesh of the DHI Danish waters hydrodynamic model

The hydrodynamic model mesh based on unstructured flexible elements, with refined resolution around the coastline of Denmark

Page 25 Figure 2.11 Numerical mesh of the Danish Waters metocean hindcast model around the Hesselø OWF

The unstructured flexible mesh is shown by the blue triangles for the hydrodynamic model HDDKW (left panel) and spectral wave model SWDKW (right panel). The Hesselø OWF development area and export cable corridor is designated by the orange outline