CFD Studies on Wind Turbine Interactions with the Turbulent Local Flow Field Influenced by Complex Topography and Thermal Stratification

This paper shows the results of CFD studies of turbulent flow fields and their effects on a wind turbine in complex terrain. As part of the WINSENT project a research test site comprising four meteorological masts and two research wind turbines is currently being constructed in the Swabian Alps in Southern Germany. This work is an essential part of the research of the Southern German wind energy research cluster WindForS. The terrain site is characterised by a densely forested escarpment and a flat plateau downstream of the slope. The met masts and 5 wind turbines are built on this plateau. In the first part, high-resolution CFD simulations are performed to separately investigate the effects of the forested escarpment and of thermal stratification on the flow field and on the wind turbine accordingly. In the second part, all the examined effects are combined for a real-life case dated March 2021. There, unstable conditions prevailed and the forest shows low leaf area densities due to the wintertime. 10 It is shown that atmospheric turbulence, forests, orographies, and thermal stratification must be considered when assessing the impact of wind turbines in complex terrain. All of these effects influence the flow field both at the turbine position as well as in its wake. Turbulent structures of the forest wake cross the rotor plane temporarily and thereby affect the turbine inflow. Moreover, convective conditions and upward flows caused by the orography have an impact on the performance output as inclined flows result in asymmetric torque distributions. The wind turbine 15 wake and the forest wake mix further downstream, resulting in a fast decay of the turbine wake. The paper also describes how the turbulent flow in the wake changes in the presence of thermal stratification.

. Overview of the numerical flow situations in the test field. In addition to the orography and the turbulent inflow plane, the wind turbine and its interaction with the flow field was also highlighted by λ2 vortex structures methods are successfully used to simulate wind fields in complex terrain (Schubiger et al., 2020). With hybrid RANS and Large Eddy Simulation (LES) methods, even small vortices detached from the ground are resolved, increasing 25 the accuracy of the simulations of the turbulent flow field in complex terrain (Bechmann and Sørensen, 2010). These hybrid RANS/LES methods are required for high-fidelity evaluations, because topographic effects such as forests and meteorological effects such as thermal stratification have a significant influence on the turbulent flow field.
Forests in complex topographies were analysed in a large-scale numerical LES study by Belcher et al. (2012a). They 30 noted that forested hills have a more significant impact on the flow situation compared to forest flows in flat terrain.
Besides, they explained that thermal stratification also has a strong influence on the resulting flow field. Belcher et al. (2012b) concluded that forested orographies downstream of the escarpment are more prone to flow separation than orographies without forest cover. Ivanell et al. (2018) conducted a numerical study to compare different simulation methods to experimental data in forested complex terrain, and to evaluate their suitability for such conditions. As 35 a result of their study, Desmond et al. (2017) found that thermal stratification also impacts the wake of forests and that turbulent kinetic energy changes fundamentally with thermal stability. The importance of considering all these topographic and meteorological phenomena in complex terrain has been confirmed by Finnigan et al. (2020), who have analysed the research and developments in this field over the last decades.
to a discrepancy of up to 5% in power generation and should therefore be accurately captured by measurements and simulations. Radünz et al. (2021) have identified the influence of local orographic effects and thermal stability on wind turbine wakes. It becomes apparent that these are also determinants of the performance output of wind turbines or complete wind farms. Barthelmie et al. (2018) conducted a study to investigate wind turbine wakes in Perdigão in mountainous terrain and discovered that they strongly depend on topography and stability. Thermal stratifications 45 have led to fundamental differences in wake trajectory measurements. The wake follows the orography more for stable conditions and less for unstable or neutral conditions. For convective conditions, the wake drifts upwards. The fact that thermal stability has a significant effect on the wake was also emphasised in the study by Abkar et al. (2016).
The WindForS project WINSENT attempts to overcome the challenges to predict more accurately the effects 50 of complex terrain on wind turbines by establishing a test site on the Swabian Alps in Southern Germany. Four meteorological (met) masts and two research wind turbines are under construction. Thus, a variety of studies are conducted experimentally and numerically. The test field has already been analysed in other studies within the framework of this project. In coarser URANS studies over longer simulation periods, El Bahlouli et al. (2020) and Berge et al. (2021) compared two selected days to Unmanned Aerial System (UAS) measurements. 55 This paper deals with highly resolved Computational Fluid Dynamics (CFD) simulations of the flow field at the test site in complex terrain and consequently on the wind turbine. In this work, new findings are presented that expand on previous studies of Schulz et al. (2016) and will provide more precise insights into the flow situation. Figure 1 shows the entire wind energy test field. Besides the forested orography, the plot also depicts the turbulent inflow plane. The fully meshed wind turbine has been integrated in its designated position and λ 2 vortex structures 60 show the strong interactions of the ambient turbulence and the forest wake with the wind turbine wake. The two already existing met masts at the test site are marked. The setup that serves as a basis for these numerical simulations is explained in the following chapter. Dividing the results chapters into two parts will enhance the understanding of the emerging effects. The first part will explain the general effects on the flow field. This includes the characteristics of the studied orography, the local forest, and thermal stratification. The investigations will show which influence  boundary layer can extend much higher than 1000 m during summer months. To realise these dimensions with also high resolutions in the relevant areas of the test site, the outer cells in y-, as well as in z-direction were coarsened via hanging grid nodes. The relevant areas at the turbine and the met masts were discretised with a resolution of 1 m. In addition, a wide area was meshed with 2 m resolution to still be able to sufficiently resolve the flow physics of large parts of the test site. In lateral and vertical direction the structured mesh is then quickly coarsened to 4 m, then 8 m and finally to 16 m to save cells and consequently computational costs. As the lower-left plot shows, 85 the highly resolved (1 m) area extends through the entire domain with constant resolution in x-direction to avoid numerical dissipation. The forest mesh is also illustrated within the grid in this section, which can be seen in the bottom area at the escarpment. The application of thermal stability implies additional requirements for the mesh.

Terrain Site & Mesh
Unstable stratification requires a very wide and high domain because of the large height of the atmospheric boundary layer and the large length scales, whereas the simulation of stable stratification requires a high resolution to 90 resolve the small eddies without losing much turbulent information through numerical dissipation. Considering these requirements without increasing the computational costs immeasurably requires a careful choice of the background mesh. The outer region of the mesh is coarsened by hanging grid nodes as described previously. The boundary layer at the bottom surface is fully resolved with y + ≈ 1.
To integrate the wind turbine into the field, as shown in the lower left plot, an additional mesh refinement in the 95 turbine's area was implemented with resolutions of 0.25 m.
The coordinate system is an inertial right-hand system that was arranged with x = 0 m at the turbine position. For detailed wind turbine evaluations, the origin of the coordinate system was shifted to the hub position (x R0 , y R0 , z R0 ), which simplifies the interpretation of the results for these studies.

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The compressible and block-structured finite volume flow solver FLOWer was used for the simulations. FLOWer was originally developed by the German Aerospace Center (DLR) (Kroll et al., 2000). Since then, the code has been extended and improved at the authors' institute for highly resolved simulations of wind turbines. Regarding the boundary conditions, at the inflow a FLOWer internal boundary condition was chosen that allows the inflow of user-defined turbulence or turbulence extracted from simulations or measurements. At the ground a friction no-slip 105 wall with the setting of a wall temperature was used. The lateral boundary conditions were chosen to be periodic. A far-field boundary condition with 0-order extrapolation was set at the top boundary and at the outlet. This allows inflow and outflow across the boundaries and behaves robustly regarding pressure gradients, which is important in turbulent flows and especially for thermal stratification. This boundary condition also suppresses possible reflections of disturbances at the numerical boundaries, which can arise from the standard far-field condition due to introducing 110 default values at the edges.
Regarding the numerical methods, the atmospheric boundary layer is simulated with the second-order Jameson-Schmidt-Turkel scheme (Jameson et al., 1981) until a height of approximately 10 m above-the-ground, because of the high aspect ratios caused by small cells and the orography. The rest of the domain is realised with a fifth-order weighted essentially non-oscillatory (WENO) scheme (Schäferlein et al., 2013). The used turbulence model is the 115 Shear-Stress-Transport (SST) model from Menter (1994). Bangga et al. (2017) obtained the most stable results for FLOWer with this turbulence model in DDES wind turbine simulations, which fit measured data best, justifying the selection. It is also the most used model in the wind energy and helicopter aerodynamics working groups at the authors' institute. An implicit dual-time stepping is applied for time integration with 100 inner iterations for each time step. This setup is valid for all simulations of this study. The Courant-Friedrichs-Lewy (CFL) number in the 120 innermost domain was set to 0.4 for the simulations without wind turbine. For the sheared velocity profile, the hub height was used as a reference position to determine the CFL number. After integrating the wind turbine into the domain, the time step was reduced to adapt it to a rotor azimuth movement of 2 • , which was needed for detailed aerodynamic evaluations of the turbine. This resulted in a CFL number of 0.2. In order to achieve high accuracy of the results, all studies in this paper were conducted with DDES simulations. Using this method, a shielding function 125 prevents the attached boundary layer from switching into the LES mode and generating grid-induced separation.
The area of the LES region and the region modelled with URANS were examined in a preliminary study. For this purpose, the resolved areas of turbulence kinetic energy k res were divided by the total TKE (k tot =k res +k mod ) for each cell in the whole domain. Thus, the study revealed that cells of the lowest approximately 0.5 m above-theground are modelled. The entire rest of the background mesh is simulated by LES. This preliminary study is valid 130 for all simulations shown in this paper.

Setup for the Comparisons with Measurements
The lower right plot of Fig. 2 shows the surface structures of the fully meshed wind turbine integrated into the background mesh with the chimera technique (Benek et al., 1986). For the mesh of the rigid turbine, reference is made to Guma et al. (2018) and Guma et al. (2020). As for the ground of the terrain, the no-slip wall boundary 135 conditions were introduced for the surfaces of the turbine. The two met masts of the test field have also been visualised in this plot to reveal a spatial impression of the test field. The first one served as a validation and comparison basis for this work. The wind turbine is about 135 m downstream of the first and about 135 m upstream of the second met mast as can be seen in Fig. 1 and 2. The two wind turbines and the other two met masts are still under construction and can therefore not serve as validation in this work. With the numerical simulations of the wind turbine, however, 140 far-reaching insights can already be gained through this study. Table 1 reveals the met mast equipment used for this work as a validation basis. The met masts serve for comparisons with numerical results and to extract turbulence characteristics to generate synthetic turbulence at the inflow. Cup anemometers, ultrasonic anemometers, and thermometers are primarily used for these studies.  orographic conditions on the plateau are very flat with only small height differences between the met masts and the wind turbine.

Forest Setup
As seen in Fig. 1, large parts of the test site, especially the escarpment, are covered by a dense forest. To be able 150 to model vegetation in the simulation, adaptations in the FLOWer code are required, which were implemented in previous works (Letzgus et al., 2018). The implementation is based on the model of Shaw and Schumann (1992) for the implementation of leaf area densities above the height.
For this purpose, as described by equation (1), a force term was added to the momentum equations to apply forest 155 modelling. The term is added to the right-hand side of the momentum equations according to equation (2). Besides the local velocities of the respective spatial direction, the force term also contains an empirical drag coefficient c d , which is usually given as 0.15 in the literature, and the height-dependent leaf area density a(z) (LAD). With an appropriate choice from measured or literature data, this parameter can model the drag that the vegetation exerts on the flow field.

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For the implementation of the forest, an additional grid structure is embedded into the background grid using the chimera technique in analogy to Letzgus et al. (2018) and Letzgus et al. (2020). In this way, the forest can be accurately defined numerically as a porous medium. Additionally, not only homogeneous forests with constant values of LAI and a(z) can be modelled, as is typical in the literature, but variable leaf area densities and tree heights can be modelled in each spatial direction. This strongly increases the accuracy of the replication of the forest shape 165 in the simulations. It is implemented by adding a force term to each cell of the forest structure depending on the foliage density and tree height. Variable leaf area densities can thus be realised in any spatial direction.
The leaf area densities of two exemplary vegetations and the implementation of forests into the CFD domain are illustrated in Fig. 3. Since the leaf area densities of deciduous forests and coniferous forests are different, the upper plot shows two curves for different vegetations. The curve with LAI = 2 shows a typical LAD profile of a coniferous 170 forest above the height. The curve indicates small LAD values that change only slightly over the height because of the relatively uniform cover. A completely different profile is shown by the LAI = 5 curve, which represents a Accordingly, the maximum drag to the wind field is expected in this area, which is valid for most vegetation types.
However, this illustrates only a very simple academic case. For example, if a mixed forest is applied, the flow field 180 will differ from a coniferous forest or a purely deciduous forest. Therefore, the vegetation species, the season, and the topology are also very important for forest modelling. On top of that, the height of the trees, the foliage densities and the distances between the trees are important for decent modelling. Thus, many factors must be considered when simulating forests. The explained approach tries to parametrise each part of the forest as accurately as possible that the results of the highly resolved simulations achieve the desired quality.
185 Therefore, the model is adapted in a way that measured tree heights and realistic foliage densities are locally considered. Varying of the local foliage density according to the season and the species is captured, too. The detailed

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The turbulence inflow data were generated with the Mann model (Mann, 1994), (Mann, 1998). The model is used by specifying the dissipation factor α 2 /3 , the turbulence intensity T i, the stretching factor Γ of the turbulence gusts, and the largest length scales L that occur. This input is used to generate a turbulence box, which is applied in this work to simulate the evaluation of the turbulent atmospheric boundary layer. In order to implement this box, the turbulent fluctuations are modelled by performing an inverse Fourier Transformation using the Mann model 195 Spectrum and the Gaussian random complex variable. A velocity profile is specified at the inlet of the domain.
After a distance of a few length scales downstream, the fluctuations generated by the Mann-box are fed in via force terms (Troldborg et al., 2014). After the propagation length of 4-5 further length scales the analytical spectrum has adapted to the real flow field with FLOWer (Müller et al., 2020), (Letzgus et al., 2020).
For the generic case studies of this work, the parameters of the Mann model were selected from experience and 200 literature values. For the subsequent real case conditions, experimental data from measurements were used to extract the turbulence parameters. The required turbulent quantities were extracted from the measurement data of the first met mast. The turbulence intensity and the length scales were extracted and, depending on the thermal stability, the dissipation factor α 2 /3 and the stretch factor Γ were adjusted.

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The Mann model in its original form is only valid for neutral conditions. However, as described by Chougule et al. (2016), adjustments can be made to capture turbulence under atmospheric stratification. For thermal stability, the parameters of the Mann model must be adjusted, as different thermal conditions also affect the length scale L, turbulence intensity T i, dissipation rates α 2 /3 and the anisotropy Γ. As the mechanically and thermally generated dissipation rates of α 2 /3 are of similar magnitudes for neutral and unstable stratification, the thermal effect of stable 210 stratification and suppressed turbulent mixing results in a reduction of this factor and thus in lower dissipation. The fit of the α 2 /3 parameters for different stratifications is reported by Chougule et al. (2016) in his study of the Rapid Distortion Theory (RDT) for buoyancy influences under stratified conditions. The stretching parameter Γ also varies for different stabilities, since the anisotropy is also much smaller for unstably stratified turbulence than for stably stratified turbulence.

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However, thermal stratification not only changes the spatial properties of turbulence. To account for atmospheric stratification, the FLOWer code was extended to allow profiles of potential temperature to be propagated through the field to represent different conditions of stability. Using this approach, a wall temperature is specified, and a potential temperature profile is fed into the flow domain at the inflow plane by adjusting the energy equations. The potential temperature field is propagated through the domain together with the atmospheric turbulence. This means that the field is initialised with a default value of the potential temperature and afterwards the temperature field is propagated through the domain. Therefore, depending on the thermal stability, the respective heat flux is simulated, which results in buoyancy. To implement an approach to consider atmospheric stratification, the momentum equations must include the buoyancy force, which depends on the change in potential temperature over height and acts positively directed upward for unstable stratification and negatively directed downward for unstable stratification. For this purpose, the momentum 230 equations are adapted analogously to Churchfield et al. (2014) in equation (2).

Governing Equations
The resulting momentum equations are represented by equation (2). On the right-hand side of the equation, besides the external force term of the forest model F F , the buoyancy force is implied. This convective force results from density differences of air parcels ρ k with their surroundings ρ 0 . The reason for these density differences are gradients 235 of the potential temperature.

Results -Part 1 Case Study of General Effects
An analysis of the different effects that have a significant impact on the flow field is presented in the first part of the results. Initially, the focus is on the forested escarpment of the test site. Subsequently, the impact of thermal 240 stratification on the test site is shown, and finally, the wind turbine is integrated into the domain.
Through this method, several parameters that determine the flow field at the test site can be examined separately.
In the second part of the results, all effects are combined and applied to a real case study.

Effects of the Forested Escarpment on the Flow Field
In the following, it will be investigated to what extent the flow field is affected by the forest at the wind energy  in foliage cover occur that affect the LAI and consequently the flow field downstream of the forested escarpment.   influences the flow field to a great extent.
The above-mentioned influences are based on simulations of summer months with an average LAI of 4.5. A variation of the leaf area densities and a comparison of the influences on the test field will be investigated in the following by using the same inflow conditions.  At first glance, significant differences of the standard deviation σ become apparent. The higher leaf area densities in the summer months result in stronger amplification of turbulence and consequently to significantly larger standard deviations than in winter months. Especially in the turbine's area at x=0 m, the fluctuations are significantly lower for the sparsely covered forest. It is worth mentioning that the propagation of the standard deviation behaves analogously for both forest covers. This means the turbulence is more amplified by the denser forest, but the forest 315 wake expands to similar ranges in height and width (for the same wind conditions) in the summer and winter months. Consequently, the forest effect is measurable at similar heights for different foliage densities. However, the atmospheric boundary layer in the forest wake will recover more quickly further downstream for the sparsely covered forest due to lower turbulence intensities.

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Next, the influence of thermal stratification on the flow field is analysed. Three simulations with the same inflow conditions and turbulence characteristics are compared. However, the buoyancy varies because of different thermal stratification conditions. As described in Sect. 2.6, the inflow conditions and turbulence characteristics differ significantly for stable and unstable conditions. The following results, however, aim exclusively to explain how thermal effects can affect flow fields. The turbulence intensity for each case was set to 8%. The results were assessed at the 325 same time or averaged over a period of four minutes. Profiles of potential temperature extracted at position x = -750 m are shown in Fig. 10. These three curves illustrate simulations of neutral, stable, and unstable stratification, respectively. The gradients of the potential temperature reveal that these are quite strong cases of atmospheric stratification. Although these are strong conditions, they are likely to occur in nature and are intended to clarify the general effects of buoyancy in this study. The depicted lines 330 belong to particular stratification conditions, which are also illustrated in Fig. 11. Based on the gradient of potential temperature from Fig. 10, the buoyancy is calculated. All three cases are investigated using the same inflow conditions. This is not the case in nature, because thermal stability also affects the properties of turbulence, such as its intensity, length scale, and dissipation. The study, however, aims to assess the 335 effects of buoyancy in general.
The flow field in neutral conditions is shown in the upper plot. Results for stable and unstable conditions are shown analogously in the middle and lower illustrations. It can be observed that atmospheric turbulence changes due to buoyancy in the flow region close to the inflow between x = -1000 m and x = -600 m. The forest wake even amplifies buoyancy effects. In the wake of the forest, the influences of buoyancy become evident. Using the flow field for neutral 340 conditions as a reference case, it is noticeable that stable stratification suppresses the mixing of the forest wake with the ambient turbulence. Consequently, the wake exhibits smaller fluctuations and does not extend to high altitudes.
Unstable stratification has the opposite effect. Thus, the wake and ambient turbulence are mixed and propagated to larger heights, resulting in higher turbulence intensities. Ultimately, unstable conditions influence the test site and the wind turbine inflow more than other conditions, which will be emphasised hereinafter.

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The standard deviations σ of the horizontal velocity are displayed in an enlarged graph of the forest wake in  For unstable conditions, the forest wake also has a stronger effect on the velocity field as shown in Fig. 12. The study of Keck et al. (2013) confirms these results. According to their research, if the wind flows over and around hills in stable conditions, there will be higher accelerations and consequently higher velocities. The lower plot shows the comparison of standard deviations versus altitude. Compared to the profile for stable conditions, there is a significant 365 increase in mixing of the air for unstable stratification. Due to the amplified turbulent mixing, the standard deviation for the entire height is higher than for stable stratification. Especially near the ground and in the forest wake this can be quantified. Besides the lower wind speed, the increased turbulence also affects the wind turbine rotor plane Transverse planes at the wind turbine position will further emphasise these effects as can be seen in Fig. 14.

Forest Effects on the Wind Turbine
In the following, interaction of the forest wake and the wind turbine is investigated for neutrally stratified conditions. flow and vegetation conditions will be analysed to develop a physical understanding of the topography-forest-turbine interaction. Figure 16 shows the interaction of the forest wake and the wind turbine. In the upper plot, the same flow situation as described before is analysed, which reaches rated turbine conditions of 11 m s −1 at hub height with a turbulence intensity of 10%. Again, this study is intended to show a summer situation with relatively high wind speeds. Here, the forest is completely leafy and accordingly has an LAI of about 4.5. Occasionally, vortex structures of the forest wake cross the rotor plane, which leads to large velocity fluctuations that may influence the rotor loads and the turbine performance negatively. In the upper plot, the dense forest causes vortex shedding at the canopy, which can randomly affect the inflow onto the wind turbine. A large area of reduced wind speeds is displayed from the upper blade tip to the ground downstream of the turbine. The forest wake quickly mixes with the turbine wake, leaving a large common wake area. In the lower plot, a comparable vertical plane is shown at higher wind speeds.

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This is a simulated real flow scenario from 31 March 2019 at 11 p.m. at the test site with average wind speeds of 16.5 m s −1 at hub height. A turbulence intensity of 9% and a length scale of 35 m was measured at the met mast, which was adjusted to the flow situation in the valley and then used as inflow data for the FLOWer simulations. As the forest is not completely leafy in spring it was modelled with an averaged LAI of 2.8. Because of the high wind speeds, the rotor blades are provided with larger pitch angles, which is the reason why the velocities of the wake are 410 not reduced as much by the turbine as in the plot above. By contrast, the inflow of the wind turbine is less affected by the sparsely covered forest, but downstream of the wind turbine a strong interaction between the forest wake and the turbine wake is readily apparent. Caused by the higher velocity differences of turbine wake and forest wake, they do not mix to the same extent as in the upper plot of Fig. 16. However, the small velocities in the forest wake affect a deflection of the turbine wake. There is a noticeable vertical wake deflection at x=130 m, which strongly 415 influences the turbine wake propagation. As a result, the forest wake and the turbine wake do not mix as strongly as they do in the upper plot, but the speed differences of the turbulent structures result in significant deflections. Thus, neutral stratification and different leaf area densities result in large forest-turbine interactions, which have a significant impact on inflow and wake.

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In the following, influences of different stratification conditions with consideration of the wind turbine are compared.
For this study, the influence of vegetation will be neglected to capture the effects of buoyancy on the inflow and wake of the wind turbine separately. For this purpose, the inflow conditions from Fig. 11 and 12 were again used.
With integrating the turbine into the flow field, the forest was removed as just described, to investigate only the influence of buoyancy and ambient turbulence on the wind turbine in complex terrain.

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Standard deviation σ (σ = σ u + σ v + σ w ) of planes perpendicular to the flow direction several rotor diameters (2D, 4D and 6D) downstream of the wind turbine are illustrated in Fig. 17 and 18. Figure 17 represents the wake cross sections for the simulations under stable conditions and Fig. 18 for unstable stratification. Through the standard deviation σ, the shape of the wake and the mixing with the ambient turbulence are explained. It becomes apparent that further downstream the fluctuations of the wake are considerably larger for unstable stratification than for 430 stable conditions. Comparing the standard deviation σ in Fig. 17 with Fig. 18, it is recognisable that already 2D downstream of the turbine the plots look entirely different. In this region primarily the blade tip vortices cause these high values of the standard deviation. For unstable stratification, the vortices spread out into significantly wider areas, whereas for stable stratification the wake keeps its circular shape longer. Further downstream, it can  and 6D) downstream of the wind turbine be assumed that the wake decays for unstable conditions more quickly, due to vortex breakdown, as analysed by 435 Troldborg et al. (2008). In stable stratification, the vortex decay will occur comparatively further downstream due to suppressed mixing, which is evident from the standard deviation at all planes.

Results -Part 2 Real Case Study: 10 March 2021
In the second part of the paper, the previously described effects on flow fields in complex terrain are investigated combined for a case study based on real-life conditions. For this study, a five-minute time period of the measurement 440 data from 10 March 2021 at 11:30 a.m. was extracted to generate inflow data in the valley. This was then propagated through the domain and compared to the experimental data. On the plateau, the flow direction is west-northwest, which corresponds with the predominant wind direction at this site. The atmosphere was slightly unstable stratified, and the forest was not leafy because of the springtime considered here. The turbulence and the velocity profile were measured by the met mast. To obtain the velocity profile at the inflow plane, the measurement data were adjusted to (2010) and Sathe et al. (2013) for slightly unstable conditions at comparable wind speeds. The stretching factor Γ was set to 3.9 and the dissipation factor α 2 /3 was set to 0.03 for higher dissipation for unstable conditions. Because 450 of insignificant wind veer, the Coriolis force is ignored.   Fig. 8. Besides, the shear is suppressed by the convective conditions in this situation, because the buoyancy 465 force drives air masses upwards. It is noticeable that the numerical results show a decent agreement compared to the measured data. The deviation of all measurement points to the simulated results remains in a range of ±1 m s −1 . The graph of the standard deviation σ above the height is shown in the right plot. Up to 60 m above-theground, the standard deviation and consequently the turbulence is significantly increased, which is shown in both the simulation and the measured data. The forest wake, which extends to higher altitudes because of the unstable 470 conditions primarily causes this effect. A stronger mixing of the ambient turbulence and the forest wake is the result.
In this region, the examined turbulence properties match well with the CFD simulations. At higher altitudes, there are deviations of the numerics and the measured data. This can probably be explained by the evaluation period in the simulations, whereby the synthetic turbulence generated stochastically via the Mann model did not exactly match the real turbulence characteristics. These turbulent data were fed into the inflow plane in the valley more 475 than 1000 m upstream of this evaluation position.
A plane through the rotor position is visualised in Fig. 21. In the upper plot, the flow field at an arbitrary moment in time is shown. The interaction of the turbine rotor, the ambient turbulence, and the turbulent wake of the forest are shown. The situation depicts the flow field 65 revolutions after the rotating turbine has been integrated into the flow field. From the turbulent structures of the forest wake, which propagate heterogeneously and expand to different 480 heights, it becomes evident that with increasing time, detaching vortex structures with low horizontal velocities cross the rotor plane. Investigating the lower plot, the turbulent inflow onto the turbine is characterised. The turbulent forest wake extends on average into heights of 45 m. The significantly increased turbulence intensity results from fluctuations at low mean velocities in the forest wake. If these structures flow through the rotor plane, the inflow will be significantly affected. This influences the loads, the power, as well as the wake. Especially in the lower right 485 rotor position, the high turbulence intensity caused by the forest wake are remarkable. The effect on the wake is explained in the following Fig. 22. The effects on power output and rotor loads follow afterwards.  Despite the lower foliage densities, the unstable conditions lead to significant mixing of the ambient flow with the forest wake, which also affects the inflow on the wind turbine. However, especially the effects on the wake are even 490 stronger. Up to x = 200 m downstream of the turbine, the turbine wake is distinguishable from the forest wake. The propagation of the blade tip vortices with increased velocities is also visible in this area. Further downstream the wake structures of the forest and the wind turbine increasingly mix and are hardly distinguishable from each other.
Considering a position that lies even further downstream, a decay of the turbulent wake is noticeable. Temporal averages show similar findings. The middle plot shows such an averaged flow solution over 60 seconds. The lower 495 plot indicates the turbulence intensity evaluated over the same period. Starting at x = 200 m, the wake contour of the turbine mixes with the forest wake to an extent that results in a uniformly spreading wake structure, which rapidly decays. Also increasing fluctuations arise from the strong mixing of the wind turbine wake and the forest wake. The turbulence production near the ground at x = -140 m downstream of the last tree row is due to transient effects: A combination of temporal flow separations and also moments with high velocities at this position causes 500 these unsteady variations of the wind.
Thus, the high turbulence intensities at these unstable conditions lead to strong fluctuations in the wake. This impact causes the wake to deform when mixing with the forest. The result is a breakdown of the wake further downstream.
The physical behaviour of the flow in the wake will be examined in more detail by looking at transverse planes in Fig. 23 and Fig. 24. The planes are extracted 2, 4, and 6 rotor diameters downstream of the turbine, respectively. 505 Figure 23 shows the averaged axial induction factor a to analyse the mean wake propagation. Figure 24 examines the standard deviation σ, which is used to evaluate the decay of the wake with increasing distance. In a distance 2D      Many conditions affect the wind turbine at the test site. The orography leads to accelerations above the escarpment.
The forest induces reduced velocities close to the ground, resulting in large shear effects and amplified turbulence.
In addition, high turbulence intensities induced by the orography and convective flows have a strong impact on the wind turbine.

Conclusions
The paper presents the results of a study of highly resolved DDES simulations of a wind energy test site in complex terrain that is currently under construction in Southern Germany. In the first part of the results, the effects resulting from orography, forests, and thermal stratification were investigated and evaluated separately. Initially, the effects on the flow field were analysed and in a second step, the fully meshed wind turbine was integrated into the flow 545 field. Subsequently, all effects were combined and applied to a real case study of 10 March 2021 in the second part of the results. The results of the simulated flow field were compared with met mast data. For the evaluation of this work, only comparative measurements of the wind field were available, as the construction of the turbines had not yet been completed on the test field at that time. Numerically, however, the wind turbine could be considered for the wind turbine were investigated. The main findings are listed below: 1) The escarpment accelerates the flow field at the altitude of the rotor plane. In combination with the upper flow field that is less influenced by the orography, a boundary layer profile with low shear versus altitude results on the plateau of the wind energy test site.

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2) At the test site, the forest has a large impact on the flow field in ground proximity. Highly turbulent fluctuations of low wind speeds in the forest wake strongly mix with the high velocity flow field above and result in highly complex and turbulent flow situations.

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3) Thermal stratification also has a strong impact on the ambient turbulence and the forest wake. Stable conditions suppress turbulent mixing, especially downstream of the forested escarpment, whereas turbulence and dispersion are strongly amplified for convective conditions. 4) By considering the wind turbine in the flow field, it has been shown that the forested escarpment impacts the 565 inflow of the turbine, as well as the mixing of the forest wake with the turbine wake. This affects wake decay further downstream. Unstable conditions amplify this effect, while in stable conditions the wake extends further downstream. 5) Taking all these effects into account when simulating real conditions of a five-minute period on 10 March 2021, decent agreements with the mean velocity profile and the turbulent statistics measured by the met masts were shown.

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6) The prevailing unstable conditions led to increased mixing of the ambient turbulent flow with the forest wake.
This had an increased effect on the inflow of the rotor plane and on turbulence amplification in the forest wake. 7) To evaluate the performance output of a virtual turbine, all of these effects had to be considered. Topographic 575 effects and convective conditions cause low shear at the rotor position on the plateau. However, vortex structures that detach from the forest occasionally cross the rotor plane and have a significant impact on performance in the lower half of the rotor. Inclined flows in the escarpment are intensified by convective conditions, resulting in increasing angles of attack and, therefore, more torque in the left rotor plane. The highly turbulent flow in the test field also impacts the turbine rotor strongly.

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This paper emphasised the importance of considering orography, vegetation, and thermal stratification in numerical simulations to resolve the flow field decently. In this way, the effects on inflow, loads, power, and wake of the wind turbine can also be predicted well.