## 3 Analysis of Wind Field Results over the Hill
### Structural Characteristics of Transient Wind Fields with Different Turbulence Models
In summary, the LES turbulence model simulates a pulsating wind velocity more accurately and can well reproduce the flow separation of the downburst flow over the hill model. Therefore, the simulation results of LES are used to compare and analyze the outflow, sinking, impinging in the wind field of the flatland and the wind field of the hill, and the process of spreading along the radial distance. Figure 13 shows the vorticity of the downburst at different moments under the flatland and its corresponding transient wind velocity fields obtained by the LES model. At T = 0.12 s, as shown in Figure 13a, during the downward impact of the airflow, it gradually expands outward due to ground obstruction, forming peak velocity and large vorticity. In addition, an obvious main ring vortex is formed near \(r\)/D = 0.75, caused by the Kelvin-Helmholtz instability (due to shear action between the impact flow and surrounding still air) [20]. At T = 0.16 s, as shown in Figure 13b, the peak velocity develops further downward and radially to near the ground, forming a high wind velocity zone in the 0.75 < \(r\)/D < 1 region. The main ring vortex also develops downward along the radial direction to the top of the high wind velocity zone. In addition, a large vortex appears near the ground in the 1.0 < \(r\)/D < 1.25 region, indicating that the peak wind velocity has a tendency to develop radially upward and flow separation occurs near the ground. At T = 0.2 s, as shown in Figure 13c, the peak wind velocity further develops in the radial direction and upward, while the flow separation phenomenon between the upper main ring vortex and near the ground is more obvious, forming a clear secondary vortex near the ground due to separation. At T = 0.24 s, as shown in Figure 13d, the peak wind velocity continues to develop to a higher position at \(r\)/D = 1.6, and the main ring vortex and secondary vortex also develop to a higher position in the radial direction. In addition, new ring vortexes and wind velocity peaks caused by the Kelvin-Helmholtz instability continue to form and develop. At T = 0.28 s, as shown in Figure 13e, as the airflow continues to develop and lift, the peak wind velocity decays, and the secondary vortex moves along the reverse direction with the rotation of the main ring vortex, also decaying. At T = 0.32 s and T = 0.36 s, as shown in Figure 13f,g, the main ring vortex continues to rotate, and the secondary vortex, resulting from flow separation, continues to move in the reverse direction and becomes progressively weaker. At the same time, main ring vortexes caused by the Kelvin-Helmholtz instability and  
Figure 14 shows the vorticity contours and their corresponding transient wind velocity contours obtained from the LES model for different moments of the downburst over the hill. At T = 0.12 s and T = 0.16 s, as shown in Figure 14a,b, since the impinging airflow is not affected by the hill model, its vorticity distribution and transient wind velocity contours are the same as those of the flatland wind field. A clear main ring vortex also appears, and flow separation occurs when the peak wind velocity develops near the ground. At T = 0.2 s, as shown in Figure 14c, as the peak wind velocity moves along the hill, the main ring vortex also moves to the hillside on the windward side and significant flow separation occurs at the contact position between the main ring vortex and the hill. At T = 0.24 s, as shown in Figure 14d, the airflow develops to the hilltop and both the peak wind velocity and main ring vortex have a tendency to develop upward. At T = 0.28 s, as shown in Figure 14e, the secondary vortex separated from the main vortex rotates in reverse at the hilltop position, similar to the occurrence and separation of secondary vortexes in flat areas. However, due to the influence of the hill model, separation and reversal of the main vortex structure occur at a higher position and its structure is more discrete.