## 3 Results
### Effects of Stability on Turbulence Spectra in Wakes  
For a better understanding on how the atmospheric stability, wind direction and with that wake position, in terms of LiDAR locations, are influencing the wake spectra, we calculated hourly spectral energy densities for the five-month period. The hourly spectra were binned and averaged over a \(10^{\circ}\) wind direction and \(0.0066\) Hz frequency intervals. The maximum in the u-spectra of the wls37 and wls65 is still visible after averaging and normalizing the data with average wind speed for stable conditions occurring during the whole measurement period and plotting the \(210^{\circ}\) to \(220^{\circ}\) bin in Figure 10. Interesting to see is that the upstream u-spectra also show a broad maximum and an elevated level of variance. The increase in variance in the upstream u-spectra can be explained by wake effects from a turbine located 1 km south-southwest and from prototype turbines with lager rotor diameter located 2 km south of wind turbine WT6. The maxima of the spectra seem to shift towards higher frequency with increasing downstream distance. The maxima in the upstream spectra are not present in the case study illustrated in Figure 8, either due to the operational status of the other turbines or due to averaging over the selected wind direction sector. A further investigation of the effect is not possible due to the lack of information on the operational status of those other turbines. Comparing the neutral and unstable cases to the stable cases, the spectra start with an overall higher variance level, but the relative increase of variance introduced by the wake is lower than in the stable cases. During neutral and unstable conditions, mixing of undisturbed air into the wake is increased and more effective, leading to a faster wake recovery. Due to mixing in the neutral case, the distinct wake maximum of the wls37 and wls65 broadens and shifts towards higher frequencies. In  
Figure 10: Composites of normalized hourly energy spectra \(u/u_{mean}\) at 80 m for wind directions between \(210^{\circ}\) and \(220^{\circ}\) under stable (left), neutral (center) and unstable (right) conditions. Dashed lines show maximum and minimum values of the data bin. Data from the upstream sonic and Windcube wls67 are illustrated in black and blue, while downstream Windcubes wls37 and wls65 are illustrated in red and green, respectively. The legend shows additionally the number of averaged hours in parentheses. The thick dashed line indicates the \(-2/3\) Kolmogorov slope. the unstable cases, the wake spectra start to recover to upstream conditions and almost follow the Kolmogorov \(-2/3\) slope at the high frequency end of the spectra. Upstream spectra are free from wake disturbances, as seen in stable cases. The spread, between the mean of the wind direction bin and its maximal and minimal members, indicates the sensitivity between the wake and beam location in dependence of the prevailing wind direction. The spread is biggest during neutral conditions. Furthermore, during neutral conditions, the slopes of the DBS spectra are less steep compared to the sonic spectra and stop following the Kolmogorov \(-2/3\) slope, which could be an averaging effect. Furthermore, measurement errors associated with the beam location could be strongest during neutral conditions where wind speeds are highest. In order to see the evolution of these wake maxima for different wind directions and therefore different upstream conditions and wake positions, Figure 11 shows the composite of all u-spectra in consecutive wind direction bins for all three Windcube. As a reference to the wls67 data, u-spectra composites of the sonic measurements are also included. Dependent on the wind direction, the sonic anemometer and the Windcube experience free-stream or wake conditions due to the different locations with respect to one of the five research turbines.