## 4 Results and Discussion
### Impact of Wind Veer and Coriolis Correction on Long Distance Wakes  
Studying the streamwise velocity, Figure 5, we can see the impact of the different configurations considered. The base case with no veer and no Coriolis correction can be seen in Figure 5a. Introducing the wind veer in Figure 5b a right turn of the wake can be seen while only including the Coriolis correction in Figure 5c shows a turn to the left. These results are those expected considering the used wind veer and the equations for the Coriolis correction. When including both the veer and Coriolis correction the resulting turn is to the right, indicating the dominating impact of the wind veer for the studied conditions. This result is further highlighted in Figure 6 that shows the contour lines of the streamwise velocity in the wake for the level 0.95. These results using LES are in line with the earlier findings from the study of [PERSON] (1955) using RANS.  
The spanwise component behind the row in Figure 7 is to the right if the wind profile includes a wind veer and otherwise it is around zero. This indicates that the major impact on the spanwise velocity is from a downward momentum transport from higher height. Inside the row, and at some distance behind, the spanwise components from the rotation of the wake behind each turbine can also be seen.  
Figure 4: The placement of the turbines (\(\bullet\)) in the two idealized wind farms in the LES domain covering 300 \(R\)\(\times\) 392 \(R\) with an equidistant region (marked with the rectangle) of 145 \(R\)\(\times\) 382 \(R\). The turbulence is added at z = 13 R, at the red line.  
Figure 6: Contour lines of streamwise velocity (W) at hub height for a row of four turbines for the cases ws, veer, ws cor and veer cor shown for the level 0.95.  
A simulation is also performed in the grid used to study a row of turbines but without turbines present for the case ws to study the development of the background flow. Part of the increased streamwise velocity outside the wake downstream in Figure 5 can be seen in the development of the background flow in Figure 8a. The background impact on the spanwise velocity is seen to be less important from a \(z\) position of about 100 \(R\) according to Figure 8b. In Figure 9 the difference with the background flow removed can be seen. The impact of the wind veer and Coriolis correction described above in Figure 5 is more clearly visible.  
Figure 7: Spanwise velocity (U) (see colorbar) at hub height for a row of turbines for cases: (**a**) ws (**b**) veer (**c**) ws cor (**d**) veer cor.  
The relative production in Figure 10 shows a slightly faster recovery for turbine number two when including the wind veer and for turbine number four a slightly higher production value when including the Coriolis correction. The overall percental change in production for the whole row can be seen in Figure 11. Including both the wind veer and Coriolis correction increases the production by 1% compared to case ws. Looking at the individual impact of including either the wind veer or the Coriolis correction, it can be seen that the largest impact on the total production comes from the former.  
Figure 8: The development of (**a**) streamwise velocity (W) (**b**) spanwise velocity (U) (mean over the equidistant region in \(x\) direction) at hub height, for case ws and no wind turbines.  
Figure 9: Streamwise velocity (W) at hub height (see colorbar) with the background flow removed, for a row of turbines for cases: (**a**) ws (**b**) veer (**c**) ws cor (**d**) veer cor.