## 3 Results
### Transient Characteristics of the Flow Field
#### 3.3.2 Evolution of the Vortex Structure  
This section further reveals the differences in the predictive ability of different turbulence modeling approaches in terms of the evolutionary characteristics of the vortex structure around the sedan. Figures 16 and 17 present the evolution characteristics of the vortex structure predicted by three turbulence modeling approaches for time periods \(t_{1}\)-\(t_{3}\) and \(t_{4}\)-\(t_{6}\), respectively (Q = 10,000). The progression of the vortex structures is highlighted in the figure with a blue dashed line, and the Z-axis component of wind speed is utilized for coloring, which is normalized based on the wind speed specified at the velocity inlet (\(U\) = 20 m/s). Six typical moments (\(t_{1}\), \(t_{2}\), \(t_{3}\), \(t_{4}\), \(t_{5}\), and \(t_{6}\)) are introduced in Section 3.2. As shown in Figure 16, only a few large vortex structures are captured during \(t_{1}\)-\(t_{3}\) based on the RNG \(k\)-\(\varepsilon\) model. The large vortex structure shedding from the edge of the sedan gradually split into several small vortices, and the vortex structures' evolution determines the main features of the flow field and the corresponding fluctuation law of the aerodynamic loads. As shown in Figure 16, many fine vortex structures and lateral vortex structure branches on the leeward of the sedan are described by the LES turbulence modeling approach. The vortex structures continuously detach from the sedan's rear and leeward side under crosswinds, resulting in fluctuations in the sedan's aerodynamic loads. The two vortex structures marked in the figure develop toward different directions; one vortex structure develops toward the rear of the sedan, and the another moves toward the lateral direction. On the basis of the IDDES turbulence modeling approach, numerous detached vortex structures are observed on the sedan's rear and leeward side (Figure 16c),  
Figure 16: Evolution of the vortex structure around the sedan predicted by three turbulence modeling approaches before the sedan drives into the dune: (**a**) RNG \(k\)-\(\varepsilon\); (**b**) LES; (**c**) IDDES (The blue dashed line marks the evolution of the vortex structure). which are mainly large vortex structures. The detached vortex structures continuously break up toward the rear side of the sedan. The vortex structure causes the leeward of the sedan to be subjected to negative pressure. However, the windward of the sedan is affected by the positive pressure, and the difference in pressure between the windward and leeward of the sedan generates lateral force. After the sedan drives into the dune section, the running scenario of the sedan switches from a uniform incoming flow state to an unsteady turbulent state, and the RNG \(k\)-\(\varepsilon\) model captures few vortex structures (Figure 17a). The vortex structure shedding near the front tire of the sedan gradually ruptured, and the small vortex structure formed with the rupture is not observed in the figure. This phenomenon indicates that the RNG \(k\)-\(\varepsilon\) model has an insufficient ability to capture small vortex structures and an inferior ability to describe the turbulent motion. The RNG \(k\)-\(\varepsilon\) model does not capture small vortex structures and cannot accurately predict the subtle changes in the flow field and present the pulsation effect of the corresponding aerodynamic loads. The RANS equations used in the RNG \(k\)-\(\varepsilon\) method adopt a statistical averaging method in turbulence, which ignores the effects of scale coupling in turbulence. There are multiple scales of vortex structures in turbulence, ranging from large-scale vortices to small-scale turbulent structures that play an important role in the flow. However, the RANS equation focuses only on large-scale structures and averages out the effects of small-scale structures, resulting in an inability to fully capture the interactions between scales and energy transfer in turbulence [38].