# Wind Characteristics in Mountainous Valleys Obtained through Field Measurement
## 3 Results
### Turbulence Characteristics
#### 3.2.4 Wind Power Spectrum  
The wind power spectrum is an important tool for measuring the wind turbulence characteristics. In this study, only the downwind pulsating wind power spectral density function was considered to obtain the degree of contribution of different scales of eddies to the turbulent energy in the pulsating wind. The Kaimal spectrum is currently recommended in the Chinese specifications. The following is an expression for the density function of the downwind power spectrum:  
\[\frac{nS_{u}(n)}{u_{*}^{2}}=\frac{200f}{(1+50f)^{5/3}} \tag{6}\]  
where \(f\) is a dimensionless parameter; \(f=nz/U\) is in the Kaimal spectrum, where \(Su\) is the horizontal downwind power spectral density function, \(z\) is the height from the ground, \(n\) is the frequency of wind, and \(u_{*}\) is the friction speed. Figure 23: Correlation between gust factor and turbulence: (**a**) the northeast side; (**b**) the southwest side. Figure 22: Gust factor ratio \(G_{v}/G_{u}\): (**a**) the northeast side; (**b**) the southwest side. Empirical power spectra commonly used in wind engineering also take the form of Harris, Davenport, and Von Karman spectra. For example, the specific expression of the Von Karman spectrum is as follows:  
\[\frac{nS_{u}(z,n)}{u_{*}^{2}}=\frac{2x}{3(1+70.8x^{2})^{5/6}} \tag{7}\]  
where \(L_{u}(z)=100(z/30)^{0.5}\) in the Japanese standard and \(x=nL_{u}(z)/\pi_{z}\). The measured spectra are fitted using a variety of existing empirical spectral formulae, and the results for the northeast and southwest sides are shown in Figures 24 and 25, respectively. The pulsating wind spectrum is usually smaller than the Kaimal spectrum, recommended by the specification in the low-frequency region, and larger than the Kaimal spectrum in the high-frequency region. The cause of this phenomenon is the complex topography of mountainous areas. The topography leads to a large turbulent component of the pulsating wind, and the energy of the turbulence is mainly distributed in the high-frequency region. Therefore, pulsating wind with high turbulence characteristics in mountainous areas with complex topography cannot be accurately and directly described using the readily available empirical function of power spectral density. After comparison, it can be seen that although the measured values deviate from the various spectral curves, the results are closest to the Von Karman spectrum. Since the Von Karman spectrum is now widely used in wind engineering, the Von Karman spectrum was used to fit the power spectrum. In this study, a two-parameter method was used to fit the power spectrum, and the expression based on the Von Karman spectrum is as follows:  
\[\frac{nS_{u}(n)}{\sigma_{u}^{2}}=\frac{Af_{u}}{\left(1+Bf_{u}{}^{2}\right)^{5 /6}} \tag{8}\]  
Figure 24: Power spectrum on the northeast side. Figure 25: Power spectrum on the southwest side. \[{f_{u}}^{2}=nL_{u}/U(z) \tag{9}\]  
where \(n\) is the frequency; \(S_{u}(n)\) is the measured spectrum value downwind; \(L_{u}\) is the integral scale; \(\sigma_{u}\) is the standard deviation of the fluctuating wind in the downwind direction, \(U(z)=u_{10}(z/10)^{\alpha};z\) is the height at a given location; \(U(z)\) is the wind speed at height \(z\); \(u_{10}\) is the wind speed at 10 m; \(\alpha\) is the wind profile index, which is taken as 0.21 based on the actual measurement results; and A and B are the parameters to be fitted. The frequency distribution histograms of parameters A and B values are shown in Figures 26 and 27. The statistical mean value of parameters A and B on the northeast side are 3.09 and 41.86, respectively. The statistical mean values of parameters A and B on the southwest side are 2.90 and 39.76, respectively. The original values of the Von Karman spectral parameters A and B are 4 and 70.8, respectively, which are quite different from the measured results. For the fitting results, the standard deviation of fitting is used to measure the error between the measured wind spectrum and various empirical spectra.