## 7 Conclusions  
Understanding the impact of atmospheric conditions on wind turbine flow dynamics is crucial for optimizing energy production and operational efficiency. Offshore wind farms introduce challenges related to larger turbines and different operating conditions. The effect of atmospheric stability on wind turbine wake dynamics has been examined in this work, in particular wake deflection and meandering. High-fidelity numerical AL-LES simulations with Mann generated turbulent inflows were used to investigate three different stabilities for turbines with and without yaw. An attempt was made to reproduce and use the Samsung S7.0-171 in the study. A successful creation of a numerical representation of the turbine has been achieved, which can be useful for later studies. However, due to a high degree of uncertainty in some parts of the validation data that are important for this work, sufficient accuracy of the AL-LES model could not be guaranteed, and the Vestas V80 turbine was used instead. As anticipated, with increasing atmospheric stability and a consequent decrease in turbulence intensity, the wake deficit also increases. Despite these differences observed for wake deficit between the neutral and stable cases, they have very similar deflected wake trajectories when the turbines are in yaw. Both exhibit a greater initial wake deflection than what is expected from the analytical wake deflection models, but this initial sharp gradient flattens out, and at 8D, good agreement is found between the numerical and analytical results. At 5D, the wake center position was found to be 0.29D, which is in excellent agreement with [PERSON] et al. [16], who reported a deflection of 0.33D for the same downstream distance. In the furthest wake position examined, at 8D, deflection increases marginally to 0.375D, exposing a new potential turbine at this location to partial wake conditions. The effect of this is made more substantial when considering that the oscillating motion from meandering has a magnitude equal to 0.25D. It was also found that the wake trajectories were very similar if the mean velocity was used to find wake centers or if the wake center position was found using the mean value of the meandering wake. This would suggest that the meandering behind yawed turbines occurs around the deflection axis. Meandering analysis was conducted at 8D for neutral and stable stabilities, while the unstable case used 4D due to the absence of a clearly defined wake. The Welch method with specific parameters provided results for cutoff frequency, peak frequency, and Strouhal number. In the neutral atmosphere, meandering behavior was similar between yawed and non-yawed turbines, while slightly larger amplitudes were observed for yaw compared to non-yaw in the stable case. Neutral simulations exhibited larger amplitudes compared to stable, non-yawed simulations. Meandering frequency appeared higher in both stable cases, supported by the peak frequency results. Results at 4D in the neutral and stable cases were similar to those at 8D, indicating some independence from downstream position. The results for stable and neutral inflows aligned well with the analytical cutoff frequency using the wake diameter. Strouhal number findings were consistent with previous studies for stable and neutral cases, but significantly lower for the unstable case. This could suggest different dynamics; however, considering the model limitations and challenges in determining the wake center, further inspection and verification are needed to draw conclusive insights. Conceptualization, B.P. and T.K.B. ; Methodology, B.P.L.A. and L.F.-G.; Software, B.P.L.A., L.F.-G. and B.P. ; Validation, B.P.L.A. and L.F.-G.; Investigation, B.P.L.A. and L.F.-G.; Resources, B.P. and T.K.B. ; Data curation, B.P.L.A. and L.F.-G.; Writing--original draft, B.P.L.A. and L.F.-G.; Supervision, B.P. and T.K.B. ; Project administration, T.K.B. ; Funding acquisition, T.K.B. All authors have read and agreed to the published version of the manuscript.