## 1 Introduction
[17], an actuator disc large-eddy simulation (AD-LES) representation of the 5 MW NREL turbine was simulated under different atmospheric conditions. This study suggested that it might not be reasonable to deflect the turbine wake through yaw in unstable conditions, as no correlation was found between the wake position and turbine yaw angle under convective conditions. In a later PhD thesis by [PERSON] [18], wind farm control under different atmospheric conditions using LES was addressed. It was found that parameters such as atmospheric stability, wind veer, shear, and turbulence intensity are important parameters to predict the wake deflection of wind turbines, and that wake deflection can increase the energy yield of a two turbine array in a neutral and stable atmosphere, while the same could not be said about a convective atmosphere. Similar results have also been reported in field campaigns by [PERSON] et al. [19] and in LES simulations by [PERSON] and [PERSON] [20] and [PERSON] et al. [21]. The Actuator Line model is particularly well-suited for simulating wind turbine wakes under varying atmospheric conditions due to its ability to accurately represent the aerodynamic forces on rotating blades without the computational overhead of fully resolving the blade geometry. This approach enables high-resolution simulations while using fewer grid cells and allowing for larger time steps, which is beneficial for studying large-scale wind farm scenarios with multiple turbines [22]. By applying the Actuator Line model in this study, we can closely examine the influence of atmospheric stability on wake behavior, particularly under yawed conditions, providing valuable insights for advancing wind farm control strategies. In the research by [PERSON] and [PERSON] [23], large-eddy simulation (LES) studies were conducted using OpenFOAM v2206 to examine wind turbine wakes under neutral and unstable atmospheric boundary layer conditions. They presented a comprehensive analysis of wake meandering, including amplitude, spectrum, and probability distribution in both horizontal and vertical planes at various downstream locations. Additionally, they explored the impact of these wake dynamics on the structural loading stability of downstream turbines through correlation analysis and power spectrum evaluation. [PERSON] et al. [24]conducted a comparative study evaluating the engineering model for the DWM against LES in the context of horizontal and vertical steering of wind turbine wakes. Their analysis involved performing LES on the IEA 15 MW wind turbine under various yaw and tilt angles to assess the accuracy and performance of the DWM model. The allure of capitalizing on the potential energy production gains of wake steering has prompted the construction of several analytical models. Analytical models for calculating the wake trajectory of yawed wind turbines have been proposed by [PERSON] et al. (2018), [PERSON] and [PERSON] (2018), [PERSON] and [PERSON] (2018), and [PERSON] et al. (2018), in chronological order. Each model was based on previous work, attempting to improve the accuracy of wake deflection estimates. A mixture of theoretical derivation with different approaches, numerical simulations, and wind tunnel experiments were used for development and testing. One of the main distinctions between models is the assumed shape of the distribution of velocity deficit and skew angle, those being a top-hat and Gaussian distribution. The Jimenez model uses the top-hat, which is often used to explain why its predictions differ greatly from the others that use the Gaussian distribution. Previous work done by the authors tested the effects of the yaw misalignment on two different wind turbines. RANS simulations were verified and validated and compared to the analytical wake deflection models described previously ([PERSON] et al., 2018).