## 3 Analysis of Wind Field Results over the Hill
### Structural Characteristics of Transient Wind Fields with Different Turbulence Models  
Figure 11 illustrates the pulsation component \(\mathrm{std}(u)/u_{j}\) of the dimensionless horizontal wind velocity computed from each turbulence model, where \(\mathrm{std}(\cdot)\) denotes the standard deviation. Overall, the computed results of each turbulence model are in good agreement with the experimental results. The pulsating wind velocity computed by the DES-SA model is smaller than that of other turbulence models in the windward region and at the foot of the hill on the leeward side. The computed results of the DES-SST and DDES-SST models at the hilltop are higher than the experimental data, which may be due to an inaccurate dissipation prediction by the turbulence model. In general, the LES turbulence model can simulate a pulsating wind velocity with higher accuracy. To obtain more intuitive results, the differences in flow separation for each turbulence model under the hill are explored by comparing the vorticity contours at different moments under each turbulence model in Figure 12. Since this paper only studies the effect of the hill on the wind field of a downburst, the impinging phase of the impinging jet (i.e., when it is not influenced by the hill model) and the fully developed phase of the flow field after completely overtopping the hill are not of concern. Figure 11: Horizontal wind velocity error at the hilltop of each turbulence model. Figure 10: Dimensionless mean wind velocity contours \((u/u_{j})\) under different turbulence models. (**a**) LES mode; (**b**) DES-SST model; (**c**) DDES-SST model; (**d**) IDDES-SST model; (**e**) DES-RK model; (**f**) DES-SA model; (**g**) SST model; (**h**) RNG model; (**i**) REA model. Figure 12: _Cont._  
Figure 12 shows the vorticity contours of the wind field obtained from simulations using different turbulence models. At T = 0.2 s, as shown in Figure 12a, the downburst  
impacts the hill and the results of each model have the same impinging position. The LES and DES-RK models separate the secondary vortex before the other models. At T = 0.24 s, as shown in Figure 12b, the structure and size of the separation vortex obtained by the DES-SST, DDES-SST, and IDDES-SST models are essentially the same, while the vortex structures obtained by the LES model are larger. At T = 0.28 s, as shown in Figure 12c, except for the DES-RK model, the flow obtained by other models has a secondary vortex separation and reverse movement. The vortex structure at the hilltop obtained by the LES model is more discrete. At T = 0.32 s, as shown in Figure 12d, the separated vortex structures obtained by each turbulence model develop along the hill to the leeward side. The separated vortex structure obtained by the DES-RK and DES-SA models is concentrated in the near-wall region of the hill, while that obtained by the LES model is more discrete and has a larger distribution range. At T = 0.36 s and T = 0.4 s, as shown in Figure 12e,f, the vortexes by each turbulence model reach the foot of the hill on the leeward side. Most of the separated vortexes obtained by DDES-SST, DES-RK, and DES-SA are distributed at higher positions and show a trend of further improvement. The separated vortexes obtained by the LES, DES-SST, and IDDES-SST models are mostly distributed near the wall and have a large distribution range. By comparing the vorticity obtained by each turbulence model at different times, it can be found that the vortex structure flow separation of the DES-SST, DDES-SST, and IDDES-ST models is similar throughout the development process. The vortex structure obtained by the LES model occurs earlier than other models, and when flowing over the hill model, the vortex structure is more discrete, and its size is smaller. However, the vortex shedding position of DES-RK is close to the near-wall position during development, and the interaction between the main vortex and secondary vortex does not develop along the vertical height, and the shear stress is small.