## 3 Analysis of Wind Field Results over the Hill
### Flow Separation of Hill  
To investigate flow separation in the wake region of a hill, two hill models (Quad-D176-H075 and Quad-D300-H075) are selected for numerical simulation. The LES turbulence model is employed in this simulation, because it can more accurately simulate pulsating wind velocity and better reproduce flow separation during the entire downburst process over the hill model.  
This paper takes the Quad-D176-H075 hill model as an example and presents its mean wind velocity and streamline contours in Figure 15. The figure shows that when the airflow flows over the front of the hill model, a recirculation zone appears at the foot of the hill on the windward side. This may be due to increased pressure and a large pressure gradient in this region. At the hilltop, where the pressure is lower, there is an acceleration of wind velocity. In the leeward region, due to the presence of a reverse pressure gradient, the velocity slows down near the ground, but no obvious flow separation phenomenon is observed.  
In order to obtain a more comprehensive understanding of the complex flow in the wake region, wind velocity data from the plane where the hill is located were subjected to a proper orthogonal decomposition (POD) analysis. Figure 16 presents the accumulated energy of the first 40 modes in the plane, which reveals that the first mode of the Quad-D300-H075 hill model accounts for nearly 20% of the total wind energy. Similarly, the first mode of the Quad-D176-H075 hill model accounts for over 25% of the total wind energy. Furthermore, the sum of the first four eigenvalues for both hill models amount to almost 50% of the total energy, indicating the importance of the early modes. Thus, the first four modes were selected to understand the flow characteristics of the hill models.  
Figure 17 shows the contours of the mean wind velocity U component and the first four modes for both hill models. A comparison of the first four modes with the mean wind velocity contours reveals large fluctuations at the hilltop and in the wake region. The first mode represents vortex shedding and is related to airflow pulsation. The amplitude of this mode reaches its maximum at and near the hilltop, with the peak amplitude near the wall of the hilltop. This may be related to the acceleration effect at the hilltop. In the second mode, there are two regions with clearly opposite velocities in Figure 17b. The region of positive velocity indicates that the airflow is flowing downstream from here, while the region of negative velocity indicates a reverse flow. That is, there is fluctuation in the same direction at the hilltop on the windward side, while opposite fluctuation occurs at the same position on the leeward side, with two peaks. These fluctuations have an S-shape and may be caused by vortex shedding on both sides of the hill. In the third mode, there are still two opposite fluctuations whose positions differ from those of the second mode, indicating  
Figure 16: Cumulative energy of the first 40 POD modes.  
Figure 15: Mean wind velocity and streamlines over the Quad-D176-H075 hill: (**a**) mean wind velocity contours; (**b**) streamlines.  
a certain phase difference. In the fourth mode, the wind velocity distributions of the two hill models differ and do not agree well, but both are similar to further diffusion of the vortex structure. In general, the first three modes show a strong similarity between the two hill models, with the first mode potentially related to an acceleration effect at the hilltop. However, significant differences appear in the fourth mode.  
Figure 17: The first four POD modes of wind velocity and mean wind velocity contours (\(u/u_{i}\)): (**a**) first order mode; (**b**) second order mode; (**c**) third order mode; (**d**) fourth order mode; (**e**) mean wind velocity contour.