## 4 Results
### Time-Varying Aerodynamic Coefficients
Figure 7: The time-varying aerodynamic coefficients of each car of the train passing the bridge with various wind barriers: (**a**) \(c_{\mathrm{s}}\) of the head car; (**b**) \(c_{\mathrm{s}}\) of the intermediate car; (**c**) \(c_{\mathrm{s}}\) of the tail car; (**d**) \(c_{\mathrm{l}}\) of the head car; (**e**) \(c_{\mathrm{l}}\) of the intermediate car; (**f**) \(c_{\mathrm{l}}\) of the tail car; (**g**) \(c_{M_{\mathrm{x}}}\) of the head car; (**h**) \(c_{M_{\mathrm{x}}}\) of the intermediate car; (**i**) \(c_{M_{\mathrm{x}}}\) of the tail car; (**j**) \(c_{M_{\mathrm{y}}}\) of the head car; (**k**) \(c_{M_{\mathrm{y}}}\) of the intermediate car; (**l**) \(c_{M_{\mathrm{y}}}\) of the tail car; (**m**) \(c_{M_{\mathrm{x}}}\) of the head car; (**n**) \(c_{M_{\mathrm{x}}}\) of the intermediate car; (**o**) \(c_{M_{\mathrm{x}}}\) of the tail car. As shown in Figure 7d-f, there was no noticeable difference in the maximum lift of the three cars in the crosswind region, but they showed different changes with time: from entering to leaving, the \(c_{l}\) value of the head car increased almost linearly with time, while the growth rate of \(c_{l}\) value acting on the intermediate car gradually slowed, and the tail car reached its maximum value and then remained until it left the crosswind region. The aerodynamic lift was mainly formed by the pressure difference between the upper and lower surfaces of the train. With the presence of wind barriers, the flow rate under the train was more directly suppressed, the lift of the train was, therefore, effectively weakened. Among them, the 4 m- and 6 m-high wind barriers almost completely eliminated the lift received by the train because the airflow both above and below the car body was synchronously filtered, but they gave a relatively high \(c_{l}\) value when the train left the crosswind region. As a combination of lateral and lift forces, the overturning moment acting on different cars passing through the crosswind region without a wind barrier showed a similar trend with different values, as exhibited in Figure 7g-h. The wind barriers always restrained the \(c_{M_{x}}\) value of the train to a large extent. It should be noted that the wind barrier with a 2 m height can cause the tail car to produce a reverse overturning moment, which was even more significant than the positive \(c_{M_{x}}\) value received without any wind barriers. It can be attributed to the effect of the side force shown in Figure 7c. A significant difference was found in the trend and the value of the pitching moments of different cars. The pitching moments of the head and tail cars were always positive, while the intermediate car showed a negative \(c_{M_{y}}\) value for more than half of the time. The wind barriers try to make the \(c_{M_{y}}\) value of each car closer to 0, but their effect was not monotonously increasing with the height of the barrier. A low yawing moment was found when the intermediate car passed through the crosswind region, and those of the head and the tail cars changed significantly because they were only connected to other vehicles at one end. The 2 m-high wind barriers effectively reduced the \(c_{M_{x}}\) value acting on the head car and had almost no effect on the tail car. A higher wind barrier reduced them to 0 and even a negative value. When leaving the crosswind area, the fluctuations that the end of the wind barrier brought to the head car were the most obvious among all aerodynamic coefficients because the difference in lateral force between the front and rear of a car was the largest. It should be noted that the reason why the intermediate car was obviously different from the head and the tail cars for