## 5 Conclusions  
The streamlined head and tail car shape design is the basis for the aerodynamic performance design of high-speed trains. In the present study, detailed wind tunnel experiments were used to verify the IDDES simulation results. Three nose lengths, standard and turbulent environments scenarios, and a total of six cases were used in this study to analyze the effects of head and tail lengths and inflow turbulence intensities on the aerodynamic performance of the train. The main findings are as follows:  
Based on the wind tunnel experiment, the IDDES numerical simulation was proved to predict the flow structure of train leeward region correctly. The maximum difference in pressure at the same section is less than 6.7%.  
When determining a high-speed train's nose length, it must weigh between drag reduction and overturning in the crosswind. The nose length of the train cannot be extended indefinitely to reduce the drag because the overturning moment of the long tail car increases dramatically under the crosswind. Under the standard flow condition of 15\({}^{\circ}\) crosswind, when the streamlined nose length increases from 5m to 10m, an increase in the length of the tail car has a greater effect on the side force coefficient and the overturning moment coefficient, and the lift and overturning moment coefficients both decrease by 72.35% and 103.63%, respectively. When the nose length of the tail car becomes shorter, the vortex core of the separation flow on the leeward side of the tail car is further away from the train body under crosswind, thus delaying the flow separation on the leeward side.  
At 15\({}^{\circ}\) yaw, increasing the turbulence intensity of incoming wind from 1% to 5% can reduce the overturning risk of the tail car. On the one hand, increasing the turbulence intensity of the incoming wind reduces the negative pressure extremum on the windward side. On the other hand, increasing the turbulence intensity of the incoming wind makes the vortex core of the separation vortex on the leeward side far away from the train body, thus achieving the effect of delayed separation. Because the vortex core on the leeward side of the head and middle cars is not fully developed, the position of the vortex cores on the leeward side of the head and middle cars is less affected.  
Figure 19: \(Q\) contours around the train with different nose lengths (\(Q\) = 60,000): (**a**) Case 1; (**b**) Case 2; (**c**) Case 3.  
When the airflow flows through the streamlined tail car, the pressure of the train body varies greatly for different nose lengths, and the maximum negative pressure at the tail car decreases as the streamlined length of the train increases.  
The location of the time-averaged vortex core for a 15\({}^{\circ}\) crosswind is approximately 0.67\(H\)-0.7\(H\) high from the ground and 0.65\(H\)-0.67\(H\) wide from the center of the train. The main frequency of the leeward vortex measured by the cobra probe ranges from 0.1 to 0.3. The transient vibration amplitude at the position of the vortex core is the largest, and the main frequency of vibration is 0.18.  
Conceptualization, B.Y. and G.C.; methodology, X.-H.X.; formal analysis, R.-D.X.; resources, X.-H.X.; writing--original draft preparation, B.Y.; writing--review and editing, G.C.; supervision, X.-H.X.; funding acquisition, X.-H.X. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key R & D program of China, grant number 2020 YFA0710903; Transport Department of Hunan Province Technology Innovation Project, grant number 202037; Hunan Provincial Education Department Project, grant number 22B0983.  
Not applicable.  
The authors acknowledge the computational resources provided by the High Performance Computing Centre of Central South University, China.  
The authors declare no conflict of interest.