## 6 Results and Discussion
### Wake Deflection  
The wake deflection is shown in Figure 16 by finding the wake center as described in Section 3.1 using the averaged velocity from the LES simulations. It is also plotted for the averaged position of the wake center at each downstream surface for the entire time series, with time steps sizes of 1 and 10 s. Filtering based on standard deviations, described in Section 3.3, is applied to the meandering signals such that the wake center measurements that are clearly unphysical are removed while keeping as much of the original measurements as possible. The deflection is then plotted against the analytical wake deflection models of [PERSON] et al. (2018), [PERSON] (2019), [PERSON] (2019), and [PERSON] et al. (2020). The equations used in these models are specified in the appendices. Comparing the wake deflection for the neutral and stable atmospheres in Figure 16a,b, they appear to be very similar. The greatest difference between the simulated deflection using the mean velocity field of the numerical solutions is found to be 2 m at 2D downstream. For the analytical solutions, the biggest differences are in the far wake, and are found to be just under 5 m for [PERSON]'s model, around 2 m for [PERSON]'s model slightly less than 1 m for the two remaining models. These findings are in agreement with the findings of [PERSON] et al. (2019), and the maximum wake deflection of about one third of a rotor diameter at 5D found in that paper is in excellent agreement with the deflection of 23.5 m or 0.29 rotor diameters found in the current results. The reduction of deflection by roughly half for the unstable case is not observed for the deflection shown in Figure 16c. It should be noted that due to the difficulties locating a wake center in the far wake of this turbine, the results are only shown until \(x=4\)D. Further downstream at 8D, the wake deflection increases to roughly 0.37D in the lateral direction. It can be seen in Figure 15 that at 8D downstream, the wake is around 2 diameters wide. This means that the mean wake will still heavily interfere with a downstream turbine and that this turbine would be in partial wake conditions. If the meandering at 8D downstream is also considered from Figure 17, this indicates that this wake would oscillate with a magnitude of 0.25 rotor diameters in both directions, which could induce additional unsteady loads on a downstream turbine. Given the difficulties in detecting the wake center in the far wake of unstable atmospheres with the wake center tracking algorithm used, this study is not able to analyze the wake deflection for this case. It is recommended for future work to also consider wake tracking algorithms aimed at detecting the wake center for this scenario. Continuing with a comparison between the simulated and analytical wake trajectories, it can be seen that the initial wake displacement is greater for the numerical solution. The deflected wakes then follow a more gentle slope to the far wake, where a better agreement with the analytical solutions is found, and at 8D a good estimate is achieved for all models but [PERSON]'s. It is interesting that the wakes of the more stable atmospheres appear to have a greater initial wake displacement than that of the unstable atmosphere. This could  
Figure 16: Wake deflection for Vestas V80 compared to analytical models, shown for (**a**) stable, (**b**) neutral, and (**c**) unstable atmospheric conditions (2018, 2019, 2020, 2020). indicate that initial wake displacement decreases with decreasing atmospheric stability, but more research is necessary to say anything conclusive. It was found in the project assignment [29] using a uniform flow RANS simulation without shear that the trajectories of the analytical solutions then followed the trajectories of the simulated wake displacement to an excellent degree, as can be seen in Appendix C. The differences between these simulations and the current ones are the turbulence model, turbulence intensity, and inflow profile.