# Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms
## 3 Results and Discussion  
### Spectral Characteristics of Typical Pressure Taps  
Following the measurement of the rectangular prisms' surface wind pressure time histories using the pressure measurement test, the Fast Fourier transform (FFT) method was used to determine the power spectral density. The spectral analysis of the wind pressure at typical pressure taps demonstrates the effects of the turbulence parameters, side ratio, geometric feature size, and three-dimensional flow on fluctuating aerodynamic forces; this aids in the investigation of energy production, transfer, and redistribution in various spatial locations [2, 3, 6, 9, 11, 19, 20, 30]. The power spectrum characteristics of typical pressure taps with various side ratios are shown for rectangular prisms with a 9# layer at 3/4 height (\(z=1.2\) m, Figure 2). Moreover, the dimensionless power spectrum of some pressure taps in the square prism is given in Figure 5, where \(S_{pi}(f,z)\) is the power spectrum density function of the measurement points, \(\sigma_{pi}\) is the root mean square (RMS) value of the pulsating wind pressure, and \(U_{z}\) is the average velocity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Wind Field**} & \multicolumn{3}{c}{**Integral Length Scale**} & \multicolumn{3}{c}{**Turbulence Intensity**} \\ \cline{2-7}  & \(L_{u}\) **(m)** & \(L_{v}\) **(m)** & \(L_{w}\) **(m)** & \(I_{u}\) **(\%)** & \(I_{v}\) **(\%)** & \(I_{w}\) **(\%)** \\ \hline BL1 & 1.216 & 0.376 & 0.301 & 12.8 & 10.7 & 8.4 \\ BL2 & 1.027 & 0.324 & 0.232 & 27.1 & 22.1 & 18.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical parameters of the turbulence field (\(z=1.2\) m). Figure 5: _Cont._The pressure taps in Figure 5 may be located using the dimensionless coefficient \(x/B\), where \(x\) is the separation distance between each tap and the stationary point. The power spectrum is primarily contorted via the incoming turbulence for the pressure taps on the windward side (Figure 5a,b), which is essentially proportional to the spectrum of the along-wind turbulence component [3, 14, 33]. The power spectrum exhibits a substantial peak as the distance from the windward corner decreases (\(x/B=0.43\)), demonstrating that the action of vortex shedding steadily increases the variable nearby wind pressure. The spectral characteristics of the fluctuating wind pressure on lateral sides are shown in Figure 5c,d. The spectral distribution trend is basically the same, with an obvious spectral peak near \(f_{s}=9.25\) Hz, and a Strouhal number of approximately \(S_{t}=f_{s}B/U_{z}\approx 0.132\), indicating the presence of an obvious vortex shedding characteristic. At higher levels of turbulence intensity (\(BL2\)), the peak of the spectrum decreases to approximately half of what it was at the \(BL1\) flow, but the spectral bandwidth increases significantly. This shows that as the turbulence intensity increases, the energy at the peak frequency is redistributed over a wider spectral bandwidth. Moreover, we discovered that the power spectrum varies depending on where it is located on the lateral side. As one moves away from the separation point, the low-frequency value of the spectrum sharply declines while the high-frequency value steadily rises. This phenomenon can be explained by the presence of large-scale, low-frequency vortices in the separated flow near the separation point; however, during the process of flowing downstream (\(x/B=0.57\to 1.43\)) the large-scale vortices are strongly disturbed by turbulence, broken up, and split into many smaller scale vortices of higher frequencies. These are accompanied by energy dissipation and transfer [3, 6, 13, 19, 20, 25, 34]. This process is more prominent in flows with higher turbulence intensities (\(BL2\)); in other words, they are flows with more extreme disruptions.