## 3 Results
### Average Wake Profiles  
In a first step, the measurements of the three static Windcube have been analyzed with respect to average wind speed and turbulence intensity (TI) profiles for different atmospheric stability conditions. As the LiDARs are aligned for the main direction, we further filtered for the wind direction interval 217\({}^{\circ}\) to 237\({}^{\circ}\) and for the situations where the wind turbine was producing power. Before averaging over the resulting cases, we normalized the wind speed profiles by the corresponding 80 m value of  
Figure 4: Wind speed ratios between the sonic anemometer measurements on M3 at 108 m and the wls67 measurements at 108 m on the basis of 10 min averages. Different wind speed intervals are color-coded. The vertical red line indicates the effect of a lightning rod on the sonic anemometer measurements. The colored solid and dashed vertical lines mark the position of the expected wake effects of the five test turbines on the wls67 and sonic anemometer measurements, respectively. the upstream LiDAR wls67 (Figure 5). This allows for a direct comparison of the average wind speed deficit in the wake region. The inflow wind profiles measured by the wls67 show the expected logarithmic wind profile for neutral conditions and a distinct increase (decrease) in wind shear for stable (unstable) conditions. The profiles measured inside the wake by the wls37 and wls65 reveal a distinct wind speed reduction, both depending on atmospheric stability conditions and downstream distance from the wind turbine. Figure 5 illustrates that the decrease in horizontal wind speed is significantly larger for stable cases than for both unstable and neutral situations. The wake deficit reaches its maximum at an altitude of 60 m, i.e., slightly below hub height. At this height, the velocity deficit reaches 40% and 30% at a distance of 1.8 D downstream in stable situations and neutral or unstable situations, respectively. Further downstream at 3.5 D, the wake has already recovered to a velocity deficit of 30% (stable) and 20% (neutral and unstable). For stable conditions, the measured deficits at 1.8 D and 3.5 D are in good agreement with the results presented by [PERSON] et al. (2010), while velocity deficits under neutral or unstable conditions are slightly below the reported ones. The strongest deficits are not only described by the average profiles, but also by the measured standard deviations. In general, the standard deviation of the wind profiles is increasing with height, which is related to the increasing horizontal probing area that is scanned during one measurement cycle. Especially during unstable conditions, where horizontal flow variations are common, the standard deviations are the largest. Furthermore, the vertical wake expansion is fairly similar during stable and neutral atmospheric stratification, as compared to a slightly higher expansion during unstable conditions. Figure 5: Mean normalized profiles of wind speed \(v_{rel}\) (upper panels) and turbulence intensity TI (lower panels) filtered for the different stability classes and averaged over all cases in the wind direction interval 217\({}^{\circ}\)–237\({}^{\circ}\). The individual 10 min average wind speeds of all three LiDAR systems have been normalized by the corresponding 80 m value of the upstream LiDAR wls67 before averaging over the number of available profiles indicated in the legend. Dots indicate the standard deviation at each measurement altitude before the normalization. Wake deficits reach an altitude of 160 m at 1.8 D, which decreases to about 120 m for measurements taken further downstream at 3.5 D. This is somewhat unexpected, as wake models in general predict a wake expansion also in the vertical (e.g., [26]). The location of the wls65 seems to be far enough downstream so that mixing of the shear layer above the rotor disk is already reducing the vertical wake extension. This reduction is in accordance with findings by [PERSON] et al.