## 6 Results of Wake Simulations  
### Case 1: Wakes of a NTK500/41 Wind Turbine  
In [PERSON] et al. [1], the wakes of a NTK500/41 wind turbine was studied experimentally and numerically using two LES methods: a classical method based on the ELLIPSYS3D flow solver [56] and an extended approach that explicitly introduces thermal and Coriolis effects as external force terms into the solver. As the wind profile predicted by MOST was observed to be much more severely sheared as compared with measurement, the classical approach applied a power law for the inlet velocity profile. The extended LES approach additionally carried out a transient precursor computation to simulate the time-varying vertical structure of the whole ABL, and it used the results of the precursor simulations to impose the mean potential temperature and velocity profiles at the inlet for wake modeling. The precursor simulations are shown to have effects on limiting the overestimated velocity gradient predicted by MOST [1]. Numerical simulations have shown that there are no major differences in wake deficit predictions between the classical approach and the extended model for stable and unstable cases. Therefore, we only compare the wake deficit predicted by the extended approach with the test models in RANS in this work. Figure 12 shows contours of wake deficits, \(\Delta U/U_{0}\), predicted by different models at hub height under stable conditions, where \(\Delta U\) is the velocity deficit in the wake and \(U_{0}\) is the inlet velocity. Simulations using the LES technology show a faster recovery wake than that in the proposed model, whereas the Laan model predicts a significant slower recovery wake with a larger deficit. One possible explanation for the stronger wake effects predicted by the Laan model is that they are due to the lower turbulence intensity predicted by the classical similarity functions. For a given reference wind speed \(U_{\text{hub}}\) and a fixed roughness length \(z_{0}\), a higher velocity gradient in the Laan model results in a smaller friction speed \(u_{*}\) and a lower turbulence intensity \(I_{\text{hub}}\) than the proposed model, and thus it weakens the wake recovery. The ambient turbulence intensities for the LES approach of 9.7% and the proposed model of 10.2% are close to the measured value of 10% while the value for the Laan model is reduced by 40% as compared to the measured data. As compared with measurements, the proposed model shows better performance than other approaches based on MOST combined with RANS for the longitudinal distance of 1-5\(D\) and the LES approach for the longitudinal distance below 3\(D\) (Figures 13 and 14). The AM, El-Askary, and Laan models overestimate the wake deficits in both vertical and lateral directions for longitudinal distances  
Figure 12: Normalized velocity distribution at hub height under the stable condition, where large eddy simulation (LES) data are modified from [PERSON] et al. [1], where \((x_{c},y_{c},z_{c})\) is the center point of the disk, \(\Delta U\) is the velocity deficit in the wake, and \(U_{0}\) is the inlet velocity. above \(2D\). All the test models in RANS fail to predict wake deficits at 4-5\(D\) downstream of the rotor. This disagreement is probably due to a combination of terrain effects and experimental uncertainties using LiDAR. According to the Space Shuttle Topography Mission (STRM)-based terrain data, the test site terrain has a downhill slope characterized by a height difference of 5.5 m from the rotor location to the most downstream cross section. As the wake has been observed to follow terrain under stable conditions [1,8], the wind speed for the longitudinal distance above 5\(D\) at the hub height is actually the value of 5.5 m above the wake center, which results in the overestimation of wake by various turbulence models in RANS. For the vertical profiles of wake deficits, Figure 14 shows that the proposed model overestimates wake deficits below the hub height at 5\(D\).