## 3 Prediction Model of Aerodynamic Coefficients  
### Flow Characteristics  
The surface pressure distribution of a moving train exposed to cross wind is demonstrated in Figure 7. It can be clearly observed that an obvious positive pressure is found on the nose region of the head car as a result of the compression effect of a running train on air ahead. However, the pressure is not symmetrically distributed but concentrated in the windward resulting from the impacts of crosswind. The negative pressure peak appears on the leeward roof corner of the head car and on the windward roof corner of the tail car, perhaps indicating there is some separate flow in this region. Furthermore, it can be seen from Figure 7b that the positive pressure is mostly distributed on the windward surface, while the negative pressure is focused on the other train surfaces, probably leading to the major side force of the train.  
Figure 6: Comparison of aerodynamic coefficients in the simulation and test: (**a**) side aerodynamic coefficient of the head car; (**b**) side aerodynamic coefficient of the middle car.  
Figure 7: Pressure distribution on the train surface (\(U=20\) m/s, \(\alpha=90^{\circ}\), \(V=300\) km/h, \(V_{R}=85.7\) m/s, \(\beta=13.5^{\circ}\)): (**a**) three- dimensional surface pressure; (**b**) pressure distribution on different surfaces.  
In order to explore the spatial flow characteristics of a moving train in a crosswind, the pressure and streamline at three typical sections on the \(x\)-axis are reported in Figures 8 and 9, respectively. As can be seen, the flow on the windward at different sections is similar but differs on the leeward. To be specific, the wake vortex (V1) of the train on the leeward gradually increases from the head car to the tail car. In fact, when the train is traveling at high speed, the airflow around the train also will move to result in the train-induced wind due to the viscous of fluids. Thus, the flow field of the train is characterized by three-dimensional structures under the combination of train-induced wind and crosswind. The wind tunnel work of an idealized train model by [PERSON] [43] also revealed that at the presence of an opening crosswind condition, the flow pattern of a moving train on the leeward is a variety of three-dimensional inclined wake vortices along the length of the car body. The simulated work of [PERSON] et al. [15] further indicated that the aerodynamic interaction resulting from a moving train and crosswind can produce the complex three-dimensional flow on the train leeward. In terms of Equations (3) and (4), the aerodynamic coupling effect of the train-induced wind and crosswind can be expressed through the resultant wind speed \(V_{R}\) and wind yaw angle \(\beta\) to dominate the flow pattern of a moving train. Figure 10 shows the surface streamlines on the train top at various resultant yaw angles. It can be clearly seen that the flow is blowing from the windward roof corner to the leeward roof corner with an inclined level, and trends to the greater incline at higher resultant yaw angles.  
Figure 8: Pressure contour of the train at different sections in the \(x\)-axis (\(U=20\) m/s, \(\alpha=90^{\circ}\), \(V=300\) km/h, \(V_{R}=85.7\) m/s, \(\beta=13.5^{\circ}\)): (a) head section; (b) middle section; (c) tail section.  
Figure 10: Streamlines on the top surface of train at different resultant yaw angles.