# The Spatial Structure of Passively Simulated Atmospheric Boundary Layer Turbulence
## 4 Results and Discussion
### Lateral Spatial Structure
Figure 5: The isotropic characteristics of the along-wind component: (**a**) lateral correlation coefficient of along\(-\)wind component; (**b**) along\(-\)wind velocity spectrum. In summary, although the statistical parameters of the wind tunnel-simulated turbulent wind field are different from the theoretical results and natural atmospheric turbulence, the lateral spatial structure can still be described approximately by isotropic turbulence theory. The coherence function, which is one of the fundamental functions for calculating the wind-induced response of wind-sensitive structures, is also different from the theoretical derivation or the field-measured value, and some targeted corrections are required. Relevant studies [16; 17; 19; 37; 38] have shown that many factors in natural atmospheric turbulence will affect the coherence function, such as turbulence, the integral scale, and the vertical wind speed gradient. Representative lateral coherences are shown in Figure 7, where the coherences for \(z=0.6\) m are plotted against \(k_{1}\). According to the results of the measured coherence function, some basic characteristics of the lateral coherence function of the simulated atmospheric turbulence can be summarized. To begin with, the lateral coherence of the simulated turbulent wind field differs from isotropic turbulence theory and the field-measured results of natural atmospheric  
Figure 6: The isotropic characteristics of the vertical component: (**a**) lateral correlation coefficient of vertical component; (**b**) vertical fluctuating wind spectrum. Figure 7: Variation of the coherence function with \(k_{1}\) for various lateral separations: (**a**) along\(-\)wind component; (**b**) lateral component; (**c**) vertical component. turbulence, both of which can be considered to approximate the horizontal homogeneous isotropic assumption. Second, the lateral distance and the turbulence integral scale have the greatest influence on the lateral coherence. The type of wind field and the height of the measuring point above the ground will have an effect on the attenuation rate, but only a minor effect on the overall distribution trend of the coherence function, which can be ignored in engineering applications. To further verify the correlation between the experimentally measured coherence and the theoretical result, Figure 8 shows the fitting conditions of the existing models. For the coherence with a measured value that is too small, the discreteness is large and the noise interference is strong, meaning the analysis significance is minor. For this reason, this investigation requires the selected coherence function \(Coh_{u}>0.1\). The fitting results show that when the dimensionless distance is \(0.04\leq\Delta y/L_{u}^{x}\leq 0.63\), the measured data are in good agreement with the theoretical models, indicating that the experimental data and the degrees of freedom in the calculation are reasonable. The isotropic turbulence theory-derived Dryden model and von Karman model can sufficiently describe the coherence of the along-wind component and have high fitting accuracy under all spacing combinations. This demonstrates that the along-wind fluctuation component can be accurately described by the theoretical coherence function model under a lateral spacing. Based on the assumption of horizontal homogeneous isotropic turbulence, the correlation of the along-wind fluctuating velocity component at any lateral spacing can be sufficiently described for the simulated turbulence field, which simplifies the analysis of the structure's wind resistance performance. In Figure 9, the value of the low-frequency region and the attenuation rate of the vertical component coherence function are different from those of the along-wind component. [PERSON]'s exponential experience model is no longer applicable. Especially when \(\Delta y/L_{u}^{x}\leq 0.26\), the fitting result is seriously smaller than the measured data, and the attenuation law in the low-frequency region cannot be accurately described.