# Wind Field Characteristics of Complex Terrain Based on Experimental and Numerical Investigation
## 5 Wind Tunnel Test Results
### Wind Power Spectra  
Due to the different undulation degree of different terrains, the energy distribution of fluctuating wind speed power spectra on different terrains may change greatly. Most of the empirical spectra used in the project are based on flat areas, so it is necessary to explore the difference between the empirical spectra and the actual spectra. Two empirical spectra are proposed by [PERSON] [46] and von Karman [47]. The comparison between the measured wind spectra and empirical spectra of the measuring points under different inflows is shown in Figure 15. From the results, the fluctuating wind speed power spectra of each measuring point are more consistent with the von Karman spectrum. The Kaimal spectrum overestimates low-frequency energy and underestimates high-frequency energy. Therefore, the von Karman spectrum is more suitable for this terrain. For each measuring point, the measured spectrum is also different under different inflow conditions. This is because the energy value at different frequencies of the wind changes obviously with different terrain, while the energy change of the downflow in flat areas is basically the same no matter which direction it enters from. Therefore, the study of the fluctuating wind speed power spectrum on complex terrain still needs to consider the incoming wind direction. Compared with other inflows, the low-frequency energy of P1 and P3 in the flat position are lower at 270\({}^{\circ}\), and the high-frequency energy of P3 increases significantly. This  
Figure 15: Normalized wind speed spectra for measurement locations at the height of 104 m.  
is because the front flow of P3 is blocked by the mountain, and the vortex scale of the air flow is significantly reduced, resulting in the increase in high-frequency energy and the decrease in low-frequency energy. The difference is that the 270\({}^{\circ}\) inflow will develop smoothly for a period of time before reaching P1, so its high-frequency energy changes little. The power spectra of P2 on the hillside is the same as the above two points, while the situation of P5 and P2 is just the opposite. P4 in the valley is not blocked under the 270\({}^{\circ}\) inflow, but is greatly blocked by mountains under the 40\({}^{\circ}\) inflow. Therefore, the low-frequency energies of the measured spectra are lower and the high-frequency energies are higher under the 40\({}^{\circ}\) inflow. In order to quantify the movement of the power spectrum energy along the frequency, three standardized frequencies \(f_{l},f_{m}\) and \(f_{u}\) are solved, which represent the cutoff frequencies of different energy intervals. This frequency is derived from the following equation  
\[\int_{0}^{\ln n_{c}}ns_{u}(n)/\sigma^{2}d[\ln(n)]-a_{c}=0 \tag{5}\]  
\[f_{c}=n_{c}Z/U(Z) \tag{6}\]  
where \(\ln\) is the natural logarithm. \(n\) is the frequency, and \(nS_{u}(n)/\sigma^{2}\) is nonnegative and integrates to one in \((-\infty,+\infty)\), and \(c=l\), \(m\), \(u\). The value of \(a_{c}\) varies with \(c\), and \(a_{l}=0.05\), \(a_{m}=0.5\) and \(a_{u}=0.95\). Hence, the bandwidth between \(f_{l}\) and \(f_{u}\), which means 90% energy interval bandwidth, is calculated from Equation (7)  
\[\Delta f=\log_{10}(f_{u}/f_{l}) \tag{7}\]  
Figure 16 shows the standardized frequency and 90% energy interval bandwidth of different measuring points under each inflow. As shown in Figure 16a, the median value of the P2 standardization frequency is the smallest, and the median values of the P4 and P5 standardization frequency are the largest. This shows that the power spectra of P4 moves to the higher frequency to the greatest extent, while the power spectra energies of P2 are concentrated in the middle and lower sections. The bandwidths of P2 and P3 are the largest, and the bandwidth of P4 is the smallest. This means that the difference between P2 and P3 is more widely distributed along the standardized frequency and narrower at P4 and P5.