## 6 Results of Wake Simulations
### Case 2: Wakes of Danwin 180 kW Wind Turbines  
The numerical results of the turbulence models based on MOST and the proposed model based on the new similarity functions are compared with the experimental data reported by [PERSON] et al. [6] in Figures 15-17. A comparison is made at distances 4.2, 6.1, and 9.6\(D\) downstream of the turbine. As the detailed rotor geometry of the Danwin 180 kW wind turbine is not available, the actuator disk model based on the thrust coefficient is applied.  
Figures 15 and 16 demonstrate the change of the wake deficit with the distance downstream of the turbine in both lateral and vertical directions. From this figure, it can be depicted that there is no discernible difference between AM, El-Askary, and Laan models at all downstream positions. As compared to measurements, these models that are based on MOST, predict larger wake deficits, and the wake deficit can be overestimated by 0.25 at 6.1\(D\) downstream of the rotor. Introducing the new similarity functions into the Laan model improves the wake prediction at 6.1\(D\) and 9.6\(D\) downstream, as compared with the models based on MOST. Note that the measured wake center or the position  
Figure 16: Same as Figure 15 but for vertical wake deficit profiles.  
Figure 15: Same as Figure 13 but for Danwin 180 kW wind turbines. All turbulence models are combined with actuator disk model (AD) based on thrust coefficient.  
of the maximum wake deficit, shifts \(\sim\)0.2\(D\) in both vertical and lateral directions at 6.1\(D\) and 9.6\(D\) downstream of the rotor. This shift of the wake center was also observed in full-scale turbine wakes with scanning-LiDAR measurements from the Crop Wind Energy eXperiment (CWEX) in Iowa [57]. The stretching of the wake structures can be attributed to the strong wind veer associated with stable conditions [6; 57]. As wind veer is a direct result of Coriolis effects caused by the Earth's rotation and the Coriolis force is not modeled in this work, all the test models fail to capture this stretching of the wake structures.  
Figure 17 shows the distribution of the normalized added turbulence \(\sigma_{u}^{2}/\sigma_{u0}^{2}-1\) in the lateral direction at hub height, where \(\sigma_{u}\) and \(\sigma_{u0}\) is the standard derivations of wind speed in wakes and in the atmosphere, respectively. A dual-peak pattern (lateral distance \(y-y_{c}=\pm 0.5D\)) is detected experimentally at 4\(D\) downstream of the rotor, as a result of rotor tip vortices and high shear production of turbulent kinetic energy caused by strong velocity gradients at the wake boundary [3; 4]. All test models capture this dual-peak pattern with lower values: the measured peaks reduce by 3 in the simulations using models based on MOST and reduce by 5 in the simulations using the proposed model. This underestimation of the added turbulence may be due to representing the turbine rotor with actuator disk instead of the actual rotor geometry. Note that the dual-peak pattern predicted by the models based on MOST can be observed at distance downstream of the rotor up to 9.6\(D\), which becomes indistinctly at 6.1\(D\) and 9.6\(D\) downstream of the rotor for both measurements and the simulations using the proposed model. As compared to measurements, the models based on MOST also overestimate the normalized added turbulence which is improved by the proposed model at 6.1\(D\) and 9.6\(D\) downstream of the rotor.