## 4 Results and Discussion
### Effect of Turbulence
#### 4.2.3 Lateral Flow Field  
As introduced above, the time-averaged flow character is an association of yaw angle and lateral flow field with different nose lengths to vortices. The vortex is identified by the transverse velocity components \((v,w)\) and the vorticity in the \(yz\) plane \((\omega_{x})\). The time-averaged results presented in Figure 12 indicate that the lateral flow field is explained by a large-scaled hairpin vortex; the vortex core is located at 0.67\(H\) from the bottom of the train. Where \(y^{*}\) (\(y/H\)) is the dimensionless width. In Chiu and Squire [35], the leeward flow field is largely insensitive to the stationary floor in the near wake. The crosswind comes over the roof and flows into the leeward side; the flow is locally dominated by rotation, the lateral wind speed reaches the extreme value of about 0.67\(H\) from the bottom of the train, and the position of this point gradually rises with the increase in wind speed. When the length of the car head is 5 m and 10 m, the vortex core positions of both leeward  
Figure 11: Time-averaged aerodynamic force coefficient with respect to different nose lengths: (**a**) \(C_{D}\) of head car; (**b**) \(C_{L}\) of head car; (**c**) \(C_{L}\) of tail car; (**d**) \(Cs\) of tail car. vortices change slightly, and the vortex nucleus coordinates of the S2 plane are (0.66\(H\), 0.67\(H\)) and (0.64\(H\), 0.72\(H\)), respectively. That is, the longer the head of the train, the closer the vortex is to the body and roof of the train in the leeward plane. The mean velocity vector field in the S2 plane is shown in Figure 12, the \(\overline{\sqrt{U_{\rm P}^{2}+U_{\rm IP}^{2}}}\) value decreases with the increase in the nose length, so the increase in the nose length can appropriately reduce the intensity of the vortex under the crosswind. The time-averaged vortex field on the leeward side at a wind direction angle of 15\({}^{\circ}\) is shown in Figure 12b. From Figure 12b, it can be concluded that the vortex core of the leeward vortex of the train is about located at 0.65\(H\), and the form is a hairpin vortex; under the wind angle of 15\({}^{\circ}\), the longer the length of the streamlined head, the smaller the vorticity on the leeward side. The identification of vortex and vorticity has been the concern of scholars, and there are three methods for vortex core identification, Q method [36], \(\lambda\) method [37] and \(\triangle\) method [38]. In this paper, we used the \(\lambda\) method [37; 39] and applied Equations (2) and (3) for the identification of vortex cores flow. \[\Gamma_{1}=\frac{1}{N}\sum_{\rm S}\sin(\theta_{M}) \tag{2}\]  
\[\Gamma_{2}=\frac{1}{N}\sum_{\rm S}\frac{[PM\wedge(U_{M}-U_{P})]\cdot\stackrel{{ \rightarrow}}{{\chi}}}{\|PM\|\cdot\|U_{M}-U_{P}\|} \tag{3}\]  
Figure 12: Velocity vector and vorticity diagram of train leeward: (**a**) S2 plane of Case 4; (**b**) S2 plane of case experimental result with 5 m train head; (**c**) S2 plane of Case 6; (**d**) S2 plane of case experimental result with 10 m head car. where \(\Gamma_{1}\) is a dimensionless scalar; \(S\) is a very small area in the limit (\(S\)\(\rightarrow\)0) and for a two-dimensional incompressible velocity field; \(\theta_{M}\) represents the angle between the velocity vector \(U_{M}\) and the radius vector \(PM\); \(S\) is a two-dimensional area surrounding \(P\), \(M\) lies in \(S\); and \(z\) is the unit vector normal to the measurement plane. \(\Gamma_{2}\) is a Galilean invariant. Figure 13 shows the spreading and vertical time-averaged vortex distribution and approximate beam flow lines in the \(y\)-\(z\) plane for S1, S3 and S5 cross-sections under 1% turbulent intensity incoming flow, where the red line is the ensemble line with the spreading flow velocity equal to 0. In Figure 13, small vortices appear at the top of the leeward side of the S1 cross-section, whose vortex field varies less with the increase in the head length, and the position of the vortex field is closer to the train body with the increase in the head length.