## 5 Simulation Details  
### Test Cases  
In this work, under stable conditions, we investigate the wakes of a 500 kW NTK500/41 wind turbine at the Rise Campus test site of DTU in Denmark [1] and three 180 kW Danwin turbines on the island of Gotland in the Baltic Sea [6]. The two test cases cover wake measured data \(1D\) to \(9D\) downstream of the turbines where \(D\) is the rotor diameter. Details of test cases are listed in Table 2.  
The first case is based on LiDAR measurements of the wakes of a NTK500/41 turbine. In this campaign, a pulsed LiDAR, which was mounted on a platform at the rear of the nacelle, pointed its laser downstream the turbine up to \(5D\) downstream the turbine. A constant downhill slope of about 0.3% was observed downstream the turbine. Inlet meteorological properties, such as wind speed, wind direction, air temperature, and atmospheric pressure, were measured from a 57-m-tall meteorological mast located upstream the turbine. The NTK500/41 turbine is a stall-regulated 500 kW wind turbine equipped with LM 19.1 m blades and its rotor speed is fixed at 27.1 rpm. Its blades consist of two kinds of airfoils: FFA-W3-XX1 (from 16 to 50% span) and NACA 63-XXX (from 60 to 100% span) [47]. Chord length and twist angle over the blades were presented in [PERSON] et al. [48]. The power curve and the thrust coefficient curve based on BEM calculations are shown in Figure 9. The power curve from BEM calculations is shown to have good agreement with the RANS computations in the full turbulence model [48] below 15 m/s and measurements [48] below 10 m/s (Figure 9). The measured thrust coefficient from strain gauges measurements [49] is also shown to have good agreements with the BEM computations above 6 m/s. In this case, we set \(z_{0}=0.095\) m, \(L=29\) m, and the hub-height reference wind speed \(U_{\mathrm{hub}}=6.76\) m/s, as presented in [PERSON] et al. [1], and apply \(C_{T}=0.83\) based on the BEM computations.  
The second case is based on wake measurements of three Danwin wind turbines using two 54 m meteorological masts, M1 and M2. In the campaign, the masts were equipped with wind sensors at 8 levels from 10 m to 53.3 m. Inlet conditions including temperature profiles were measured on mast M1, whereas wake profiles of the three turbines were measured on mast M2. The distances from the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Wind Turbine** & \(D\) **(m)** & \(H\) **(m)** & **Measurements** & **Wake Range** \\ \hline NTK500/41 & 41 & 36 & LiDAR scanning & \(1D\) to \(5D\) \\ Danwin & 23 & 35 & Mast measurements & \(4.2D\), \(6.1D\), and \(9.6D\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details of measurements in the two test cases.  
Figure 9: Performance curves of the NTK500/41 turbine.  
three turbines to mast M2 are 4.2\(D\), 6.1\(D\), and 9.6\(D\), respectively. In this case, we set the roughness length, the Obukhov length, the reference wind speed and the thrust coefficient to be 0.0005 m, 35 m, 8 m/s and 0.82, respectively [6; 50]. The detail information of test cases is shown in Table 3 where TI\(=\sqrt{\frac{2}{3}k_{\text{hub}}/U_{\text{hub}}}\) is the ambient turbulence intensity at hub height and \(k_{\text{hub}}\) is the corresponding hub-height turbulence kinetic intensity [16]. The measured ambient turbulence intensity in the first case is \(\sim\)10%.