## 4 Results and Discussion
### Fluctuating Wind Characteristics
#### 4.2.4 Coherence Function  
The fluctuating wind coherence function is used to assess the correlation of wind loads at different locations on a structure, which aids in predicting the vibration behavior of bridges under wind action. The coherence function is defined as the ratio of the cross-spectral density to the auto-spectral density of fluctuating wind speeds, as expressed in Equation (7) [33]. By fitting the experimental values with the modified coherence function Equation (8), the values of parameters \(K\) and \(C\) can be obtained, where \(K\) represents the coherence at a reduction frequency of zero and \(C\) is the decay coefficient. Under uniform inflow conditions, the variation in wind speed across space is very minimal. After investigation, the correlation between fluctuating wind speeds at different locations is low, and the coherence function between two measurement points on the bridge is very weak in uniform inflow cases. When the coherence function is weak, the effectiveness of formula fitting is also poor. Therefore, only the coherence at various locations on the bridge under ABL inflow conditions is displayed in this section. When the wind direction is \(0^{\circ}\), the coherence functions between two points with the same spacing but at different locations on the main beam under different oncoming wind speeds are presented in Figure 43. It can be observed that as the wind speed increases, the value of \(K\) gradually increases, and the value of \(C\) also increases. The increase in \(K\) indicates that the coherence between the two points strengthens with the increase in wind speed. A strong coherence function means that different locations of the structure may be simultaneously influenced by wind loads, leading to a more significant overall structural response. The larger decay coefficient \(C\) indicates that the coherence decreases more rapidly with increasing distance, implying that the two points must be very close for the coherence to be significant. In engineering practice, special attention should be given to areas with strong coherence but a high decay coefficient, and a severe local impact can be caused on the bridge. Additionally, it is noted that when two points are at different locations but with the same spacing, the results of the coherence function are quite similar, which suggests  
Figure 41: Turbulent integral scale of the main beam under uniform inflow with different wind speeds and directions. Figure 42: Turbulent integral scale of the main beam under ABL inflow with different wind speeds and directions. that in the flow field of mountain valleys, the size of turbulent vortices for two points at a fixed distance may be consistent. When the wind direction is \(30^{\circ}\), the coherence function at the same locations is investigated, as shown in Figure 44. Notably, at the oncoming wind speed of 14 m/s, the two points on the main beam exhibit strong coherence and significant decay, and the variation in the coherence function with wind speed is essentially consistent with that at \(0^{\circ}\) wind direction. However, for two points at the same distance, the decay coefficients at half span and five-sixths span are much higher than those at one-third span and two-thirds span. This phenomenon is caused by the obstructive effect of the mountains in a \(30^{\circ}\) wind direction, which affects the effective distance of coherence. The coherence functions at different wind speeds under the \(180^{\circ}\) wind direction are illustrated in Figure 45. The coherence function between the two points also increases with the increase in the oncoming wind speed. Since the main beam is completely on the leeward side of the mountain in the \(180^{\circ}\) wind direction, the coherence between the two points is very weak, and the decay coefficient is also high. This may be due to the strong turbulence on the leeward side of the mountain, which leads to a reduction in wind coherence between different locations, thereby weakening the coherence function.