## 3 Results
### Effects of Stability on Turbulence Spectra in Wakes
The positions in relative rotor diameters for the different directions are summarized in Table 1.  
Figure 11 presents composites of the spectral energy density of the along-wind component for 10\({}^{\circ}\) wind direction bins. Northerly wind directions place the Windcube wls67 downstream of the research turbine row, while for southerly winds, the Windcubes wls37 and wls65 are located downstream and affected by the wakes. This upstream or downstream location of the LiDARs is clearly visible in the u-spectra with increased levels of variance and wake peak frequencies fluctuating around 0.02 and 0.05 Hz in different wake positions. In the case of south to south-westerly winds, the upstream measurements of the wls67 are disturbed by far-wake effects of the further upstream prototype wind  
Figure 11: Composites of hourly energy spectra of u at 80 m for all wind direction bins from wls67, wls37 and wls65 (from left to right). White circles indicate the maximal spectral energy density of each direction bin. Additional subplots show wind direction bin averaged horizontal wind speeds at 108 m (blue in (m\(\cdot\)s\({}^{-1}\))), power output (black in (MW/100)) and blade pitch angle (gray in (\({}^{\circ}\))) of wind turbine WT6 and the number of averaged hours in each bin for wls67 (blue), wls37 (red) and wls65 (green). turbines. Nevertheless, the level of variance still increases for the downstream LiDARs wls37 and wls65 in these conditions. Distinct maxima are only visible in the wls65 data furthest downstream. In addition to the u-spectra, the power production and blade pitch angle of wind turbine WT6 and the horizontal wind speed of the sonic anemometer at 108 m are also available and averaged over the same wind direction bins. Easterly and westerly winds show the lowest production of turbine WT6 since it is operating in the wake of turbine WT9 or turbine WT5, respectively. Maximum production seems to be linked to north-westerly winds coming from offshore and passing only a short distance over land before reaching the turbines. However, less data are available for these wind directions. Filtering the hourly u-spectra presented in Figure 11 with respect to the prevailing atmospheric stability conditions (see Table 2) allows for a more detailed discussion of the wake peak frequency. The above presented hypothesis of consistent wake maxima over long distances under stable conditions, the shifted wake maxima towards higher frequencies under neutral conditions and the faster wake recovery under unstable conditions, seems to be consistent over all wind direction bins (Figures 12 to 14). Stable conditions are generally characterized by lower wind speeds and blade pitch angles, resulting in the lowest levels of variance, but rather distinct maxima indicated by the white dots in the composites (Figure 12). Peak frequencies vary between 0.03 and 0.05 Hz in almost all bins associated with a turbine wake. In neutral conditions, wind speeds are generally higher, leading to high variances in the u-spectra (Figure 13). Wake peak frequencies tend to shift towards higher frequencies. For south-westerly winds, wind speeds are highest, resulting in the highest power production, which shows that the turbine row was clearly designed for those conditions. In unstable conditions, southerly variances are reduced with slightly lower wind speeds compared to neutral conditions (Figure 14). Far-wake spectra measured by the wls67 seem to have recovered to almost free stream conditions with a classical energy decay from lower to higher frequencies. The elevated variance of southerly winds has been smooth over a wider range of wind direction bins, including westerly winds. Data of wls37 and wls65 in unstable conditions show wake peak frequencies leaning towards lower values, but are too sparse for further interpretation. Figure 12: Composites of hourly energy spectra of u at 80 m for all wind direction bins from wls67, wls37 and wls65 (from left to right) filtered for stable wind conditions.