# The Spatial Structure of Passively Simulated Atmospheric Boundary Layer Turbulence
## 4 Results and Discussion
### Lateral Spatial Structure
When \(\Delta y/L_{u}^{x}\leq 0.26\), the Dryden and [PERSON] coherence function model can describe the distribution trend of the vertical component coherence function, but the fitting result in the low-frequency region is higher than the measured data. When \(\Delta y/L_{u}^{x}>0.26\), the fitting deviation gradually becomes significant as the distance increases. Figure 9: _Cont._  
The fitting results of the coherence function show that the vertical fluctuating component is significantly affected by the shear stress of the boundary layer, resulting in the rotation or stretching of the vortex, meaning that the turbulent spatial structure under a horizontal lateral spacing gradually becomes \"nonisotropic\". Given the importance of the coherence of the vertical component in wind-induced vibration analysis, and the fact that the accuracy of the existing empirical or theoretical model cannot meet the requirements of engineering practice, some improvements are required. Based on the theory of isotropic turbulence, scholars have modified the lateral coherence function model of grid turbulence to describe the influence of nonisotropic components on the spatial structure of turbulence. Although the 3D structure of atmospheric boundary layer turbulence is more complicated than grid turbulence, it is a simple and effective method for improving the existing theoretical model based on the horizontal isotropic turbulence assumption. This study examined the stretching effect of nonisotropic turbulence components on vortices of various scales using correction of the turbulence integral scale and wave number and attempted to extend this correction method to atmospheric boundary layer turbulence. Based on the [PERSON] coherence model, the modified model form of the vertical component is  
\[Coh_{w}(k_{1},\Delta y)=\frac{2^{1+\zeta/2}}{\Gamma(-\zeta/2)}\cdot\left[\eta _{\chi}^{-\zeta/2}K_{\zeta/2}(\eta_{\chi})-\frac{\eta_{\chi}^{1-\zeta/2}K_{1+ \zeta/2}(\eta_{\chi})}{B_{K}}\right] \tag{15}\]  
\[\eta_{\chi}=\frac{\Delta y\beta}{a_{1}L_{u}^{x}}\cdot\sqrt{1+(2\pi k_{1}a_{1} L_{u}^{x}/\beta)^{b_{1}}B_{K}}=1+\frac{8}{3}\cdot(2\pi k_{1}a_{1}L_{u}^{x}/\beta)^{b_{1}} \tag{16}\]  
Using a similar definition, a modified model based on the [PERSON] theoretical model can be obtained:  
\[Coh_{w}(k_{1},\Delta y)=\theta_{\chi}K_{1}(\theta_{\chi})-\frac{\theta_{\chi }^{2}}{B_{D}}K_{0}(\theta_{\chi}) \tag{17}\]  
In the above formula, the expression of the modified parameter is as follows:  
\[\theta_{\chi}=\frac{\Delta y}{a_{2}L_{u}^{x}}\cdot\sqrt{1+(2\pi k_  
According to the fitting results of the vertical component coherence function in the BL3 turbulent wind field at \(z=0.9\) m, it can be found that the modified models are in good agreement with the measured results. The improved von Karman and Dryden theoretical models can describe the vertical component coherence function distribution at any interval and correct the problem of overestimating the value of the low-frequency region at large intervals. Table 4's coefficients take into account all influencing factors and average the fitting results for each measurement height and spacing combination. Each parameter varies with the wind field and measurement height, but the distribution law is obvious and can be approximated as a constant. In the modified von Karman model (Equation (15)), the