## 4 Results and Discussion
### Fluctuating Wind Characteristics
#### 4.2.3 Turbulent Integral Scale  
The turbulent integral scale refers to the characteristic length scale at which two turbulent fluctuating velocity vectors are spatially correlated, reflecting the range of energy transfer and momentum exchange in turbulence. The methods currently used to obtain the turbulent integral scale generally include the von Karman spectral fitting method and the correlation function integration method based on the Taylor frozen turbulence hypothesis. The von Karman wind spectrum is conducted in the frequency domain, and information about the distribution of turbulent energy across different frequencies is provided. In contrast, the auto-correlation function method, which analyzes in the time or space domain, may not reveal the spectral characteristics of turbulence. Therefore, when the power spectrum satisfies the von Karman wind spectrum, the turbulent integral scale results obtained through von Karman spectral fitting are considered superior [31]. The expression for the longitudinal wind von Karman wind spectrum is given by Equation (6) [32]. During the analysis of the power spectrum at various points on the bridge, it was found that the von Karman wind spectrum aligns well with the power spectra. The fitting results for some cases at the midspan of the bridge under a 0\({}^{\circ}\) oncoming direction for both uniform and ABL inflows are demonstrated in Figure 36. Consequently, the turbulent integral scales at various locations on Jinqi Bridge are obtained through fitting the von Karman spectrum. The turbulent integral scale at the southwest bridge tower is shown in Figures 37 and 38. When the oncoming wind is uniform, the turbulent integral scale increases with the increase in height. The higher the oncoming wind speed, the larger the turbulent integral scale, indicating that the formation of large-scale vortices may be promoted by the higher wind speeds. When the oncoming flow is ABL inflow, the turbulent integral scales for the 0\({}^{\circ}\) and 30\({}^{\circ}\) directions also tend to increase with the rise in wind speed. However, when the wind direction is 180\({}^{\circ}\), the variation in the turbulent integral scale with wind speed is not significant. Figure 35: Longitudinal fluctuating wind power spectra of the main beam under ABL inflow with different wind speeds and directions. The turbulent integral scale at the northeast bridge tower is illustrated in Figures 39 and 40. When the oncoming flow is uniform, the turbulent integral scales at the northeast bridge tower for \(0^{\circ}\) and \(30^{\circ}\) wind directions decrease as the oncoming wind speed increases. Combined with the result in Figure 26 that higher wind speeds correspond to lower turbulence intensity, this indicates that at this location, the processes of airflow mixing and diffusion primarily occur at smaller scales under high-wind-speed conditions. When the oncoming flow is ABL inflow, the turbulent integral scale at the northeast bridge tower increases with height. The variation in the turbulent integral scale with the oncoming wind speed is not remarkable for oncoming flows from all directions. Figure 36: Comparison between the power spectrum and von Kármán spectrum fitting results at 1/2 span of the main beam. Figure 37: Turbulent integral scale of the southwest tower under uniform inflow with different wind speeds and directions. Figure 38: Turbulent integral scale of the southwest tower under ABL inflow with different wind speeds and directions. The turbulent integral scale at the main beam is shown in Figures 41 and 42. It is noted that when the oncoming wind is uniform and the wind directions are \(0^{\circ}\) and \(30^{\circ}\), with the midspan of the main beam as the dividing line, the turbulent integral scale increases with the wind speed in the left half-section while decreasing with the increase in the right half-section, as shown in Figure 41,b. This result indicates that the variation in the turbulent integral scale with oncoming wind speed is greatly influenced by the topography.