# Research on Wind Field Characteristics Measured by Lidar in a U-Shaped Valley at a Bridge Site
## 4 Results and Discussion
### Wind Direction
#### 4.2.2 Wind-Direction Deflection  
Taking the midspan position as an example from Figure 15, the wind direction rose, and it can be seen that the wind direction at the bridge deck height is significantly affected by the U-shaped valley terrain, and the wind direction is highly dispersed, mainly north and southeast. As height rises, the wind direction dispersion decreases, and the main wind turns to the right and tends to the southwest. In order to study the torsion law of wind direction with height, the following analysis was made:  
First, the wind-direction deflection rate \(\alpha\) is defined: the wind direction of the oncoming flow would deflect with height due to the influence of U-shaped valley topography, Coriolis force, and other factors, which is represented as the change rate of the angle with the unit height. The smaller the absolute value \(\alpha\) is, the more violently the oncoming wind direction is deflected by disturbance, as shown in Figure 16 and Equation (4).  
\[\alpha=\frac{\partial y}{\partial x} \tag{4}\]  
Take the derivative of Equation (4),  
\[y=\alpha x+b \tag{5}\]  
where \(x\) is the wind-direction angle (\({}^{\circ}\)), \(y\) is the height (m), \(\alpha\) is the wind-direction deflection rate (m/\({}^{\circ}\)), and \(b\) is the undetermined constant (m).  
Further, 24 h is taken as the unit time to calculate the average (AVE) and standard deviation (STD) of the wind direction. Taking VWT-1 and VWT-3 as examples, as shown in Figure 17, the 150 m height is the turning point, and the AVE and STD of wind direction have a numerical mutation, which may be due to the blocking effect range of mountains in the direction of incoming flow being about 150 m. On the one hand, below 150 m, the maximum AVE wind direction is about 225\({}^{\circ}\) and the maximum STD is about 94.3\({}^{\circ}\). On the other hand, above 150 m, the AVE and STD of wind direction fluctuate weakly; the AVE wind direction increases about 14%, from 185\({}^{\circ}\) to 211\({}^{\circ}\), and the STD of wind direction goes down by 8\({}^{\circ}\)and 4\({}^{\circ}\).  
Figure 15: Wind direction rise diagram at VWT-3.  
Next, taking 150 m as the cutoff point, the data is divided into two parts, the first stage and the second stage. Statistical and fitting analysis was made for the AVE wind direction. Deflection of wind direction with height is treated as a linear piecewise function, as shown in Figure 18 and Equation (5).  
Figure 16: Sketch of wind-direction deflection rate.  
Figure 17: Average and STD of wind direction.  
\[y=\{\begin{array}{c}-10x+200(x\leq 185)\\ 65x/3-3860(185<x\leq 245.5)\end{array}\]  
The fitting results are shown in Figure 18 and Equation (5). The wind-direction deflection pattern shows two linear relations of positive and negative. Below the height turning point in the first stage, the wind deflection rate \(\alpha_{1}\) is \(-10\), and in the second stage, the wind deflection rate \(\alpha_{2}\) is \(65/3\), \(|\alpha_{2}|\approx 2.17|\alpha_{1}|\) According to the definition of \(\alpha\),below 150 m, the wind deflection is more dramatic, approximately 2.17 times that above the cutoff point.