## 4 Results and Discussion
### Effect of Turbulence
#### 4.2.3 Lateral Flow Field
The vortex scale appearing on the S3 surface in Figure 13 is larger than the S1 surface vortex, which is a longitudinal leeward vortex and is located closer to the train body as the head length increases. On the S5 plane, in Figure 13, in addition to the longitudinal leeward vortex, there are two other vortices on the leeward side, located at the top and bottom of the leeward side, but the top vortex is not obvious in Case 2 and Case 3. Overall, with the increase in the nose length of head car, the vortices affecting both lift and side forces are closer to the car, resulting in a larger aerodynamic SD for the long nose length of head car. Figure 14 shows the mean vortex distribution and approximate beam flow lines in the \(y\)-\(z\) plane in the spreading and vertical directions for the three cross sections S1, S3 and S5 under 5% turbulent intensity incoming flow. Comparison with Figure 14 reveals that the increase in turbulence intensity has less effect on the location of the vortex core on the leeward side of Case 4 and Case 5 because the longitudinal vortices are relatively far away from the bottom vortex core. However, as the streamlined length of the train wake reaches 10 m, the longitudinal vortex in Case 6 is closest to the train body, compressing the bottom vortex. Moreover, because the rotation direction of the bottom vortex is counterclockwise, thus strengthening the counterclockwise moment on the leeward side, the tail car lift force increases and the side force decreases. At the same time, due to the increase in incoming turbulence intensity, the turbulence increases the curvature of the shear layer by interacting with the shear layer separated from the top of the train, which makes the shear layer closer to the leeward side and reduces the side force and overturning moment, which improved the stability of the train. Increasing the turbulence intensity of the incoming wind makes the vortex core of the separation vortex on the leeward side far away from the vehicle body, thus achieving the effect of delayed separation. According to Figure 13c,f,i, it can be concluded that when the nose length of the tail car gets shorter, the vortex core of the separation flow on the leeward side of the tail car is further away from the vehicle body under 15\({}^{\circ}\) crosswind, thus delaying the flow separation on the leeward side. Comparing Figure 13i with Figure 14i, increasing the turbulence intensity of the incoming wind will make the vortex core of the separation vortex on the leeward side far away from the vehicle body, thus achieving the effect of delayed separation. Figure 15 shows streamlines projected on the surface of the head train. When the airflow is through the streamlined head, the separation line is marked as SL. Flow separation occurs at the top of the train, followed by turbulent reattachment in a small area on the leeward side. Compared with Case 2 and Case 3, the separation lines at the top and bottom of the leeward side of the head car of Case 1 are farther apart. The separation lines of Case 1 cannot converge at the leeward side of the head car, which also leads to the large negative pressure value at the bottom of the head car of Case1 and the small lift coefficient of the head car. The increase of turbulence intensity has more influence on the lift coefficient of the head car and less influence on the side force. Figure 14: Streamlines and time-averaged vorticity field under 5% turbulence intensity showing the circulation regions projected onto the \(y\)–\(z\) planes: (**a**) S1 of Case 4; (**b**) S3 of Case 4; (**c**) S5 of Case 4; (**d**) S1 of Case 5; (**e**) S3 of Case 5; (**f**) S5 of Case 5; (**g**) S1 of Case 6; (**h**) S3 of Case 6; (**i**) S5 of Case 6.