## 4 Results and Discussion
### Mean Wind Characteristics
#### 4.1.2 Wind Yaw Angle  
The wind yaw angle \(\alpha\) represents the horizontal angle between the direction of the wind reaching the bridge and the oncoming wind direction, as defined by Equation (3). The wind yaw angle is a fundamental parameter for studying the wind-induced vibrations of bridge components in different directions. The wind acting on the bridge from different directions is clearly reflected by the wind yaw angle; thus, the wind loads in each direction can be determined. The distribution of wind yaw angles on the southwest bridge tower is shown in Figures 12 and 13. When the oncoming wind is uniform, the wind yaw angle shows a trend of first decreasing, then increasing, and then decreasing again with height, which is related to the undulations of the terrain. The wind yaw angle exhibits minimal variation with the oncoming wind speed, with the obtained curves largely overlapping. When the oncoming wind is ABL inflow, at the locations \(y/H=0.25\), \(0.5\), and \(1\) under the \(180^{\circ}\) wind direction, there is a trend for the wind yaw angle to decrease with increasing oncoming wind speed, and the change is relatively small. There is only about a \(1^{\circ}\) difference in the wind yaw angle between oncoming wind speeds of \(6\) m/s and \(14\) m/s.  
The distribution of wind yaw angles on the northeast bridge tower is shown in Figures 14 and 15. Influenced by the irregular terrain, the distribution of wind yaw angles on the northeast bridge tower is also very complex. Overall, the wind yaw angles on the northeast bridge tower are relatively small and affected by the oncoming wind speed. When the oncoming wind is ABL inflow and the wind direction is \(180^{\circ}\), the wind yaw angle tends to decrease with the increase in incoming wind speed, as shown in Figure 15c.  
Figure 11: Wind speed amplification factor of the main beam under ABL inflow with different wind speeds and directions.  
Figure 10: Wind speed amplification factor of the main beam under uniform inflow with different wind speeds and directions.  
Figure 14: Wind yaw angles of the northeast tower under uniform inflow with different wind speeds and directions.  
Figure 12: Wind yaw angles of the southwest tower under uniform inflow with different wind speeds and directions.  
Figure 13: Wind yaw angles of the southwest tower under ABL inflow with different wind speeds and directions.  
Figure 15: Wind yaw angles of the northeast tower under ABL inflow with different wind speeds and directions.  
The distribution of wind yaw angles on the main beam is shown in Figures 16 and 17. When the oncoming wind directions are \(0^{\circ}\) and \(30^{\circ}\), the wind yaw angles on the main beam remain unchanged with the oncoming wind speed for both uniform and ABL oncoming inflow. However, when the oncoming wind is on the leeward side of the mountain, which corresponds to the \(180^{\circ}\) wind direction, the wind yaw angle tends to decrease with an increase in oncoming wind speed. This may be due to the flow field structure on the leeward side of the mountain being altered with the increase in oncoming wind speed, resulting in different distributions of wind yaw angles on the main beam.  
\[\alpha=\arccos\left(\frac{U_{x}}{\sqrt{U_{x}^{2}+U_{y}^{2}}}\right) \tag{3}\]