## 1 Introduction  
Offshore wind energy is emerging as the next large-scale energy production device, with better economic conditions, technological development, and favorable policies opening new markets and areas for production. According to the most recent estimates of the International Energy Agency (IEA), total offshore wind capacity is set to more than triple by 2026, reaching almost 120 GW of installed capacity, which would account for one fifth of the total capacity of installed wind energy [1]. When more wind farms with bigger turbines are being built offshore, the occurrence and importance of different atmospheric conditions are increasing. This makes understanding how this affects the flow dynamics of wind turbines more important in order to optimize energy production and the operation of wind farms. As mentioned in a review paper by [PERSON] et al. [2], it has been shown in numerous papers that the convective boundary layer displays stronger wake meandering and faster wake recovery compared to the neutral and stable atmospheric boundary layers [3; 4; 5; 6; 7; 8; 9; 10]. Wake meandering is associated with one of the main impacts that stability has on the flows, namely changes in length and velocity scales of the atmospheric turbulence. Faster wake recovery is attributed to the increase in turbulence intensity, another consequence of decreasing stability, as found by [PERSON] and [PERSON] [9]. They found that not only the magnitude but also the spatial distribution of the mean velocity deficit, turbulence intensity, and turbulent momentum fluxes were affected. In the present study, the Mann turbulence model is used to replicate different sized eddies in the different inflows and the corresponding spatial coherence. There are two primary theories that attempt to explain the meandering of wind turbine wakes. One is that the wake is passively advected by large-scale turbulent motion originating from the inflow [11]. The other is an observation that wake meandering behind wind turbines exhibits similar behavior to that of vortex shedding behind bluff bodies in high Reynolds number flows. The non-dimensional Strouhal number represents the frequency associated with this vortex shedding, and its expected value for flow around a solid circular disk is around 0.12, the same as for a turbine with a very high tip speed ratio. As the tip speed ratio decreases, \(St\) increases. [PERSON] et al. [12] found experimentally that for a variety of turbine configurations, \(St\) was in the range of 0.12 \(\to\) 0.2. [PERSON] et al. [13] found \(St=0.16\) to be a recurring number both in their computational fluid dynamics (CFD) study of their wind turbine and in many other studies of seemingly unrelated flows presented in their literature review. Wake steering shows potential in improving wind farm efficiency and reducing wake losses, both in wind tunnel studies [14] and field campaigns [15]. The research into wake steering under different atmospheric stabilities has not been as extensive as for the non-yawed conditions, with a few notable exceptions. [PERSON] et al. [16] performed experimental and numerical measurements at the The Scaled Wind Farm Technology (SWFT) facility with the aim of measuring wakes and wake deflection resulting from yaw misalignment under a variety of atmospheric conditions. Actuator line large-eddy simulation (AL-LES) simulations are initially run in order to better plan and predict subsequent experiments using light detection and ranging (LiDAR) measurements. These experiments indicated that wake deflection will be strongest under stable to neutrally stratified conditions, and the enhanced mixing of the unstably stratified conditions decreases the amount of expected deflection. Under stable and neutral conditions, a maximum wake deflection of about one third of a rotor diameter is expected 5 rotor diameters (5D) downstream, while this is reduced by roughly half under convective conditions. In a study by [PERSON] et al.