# Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms
## 3 Results and Discussion
### Spectral Characteristics of Fluctuating Aerodynamic Forces  
The fluctuating aerodynamic forces in three directions (along-wind fluctuating load, across-wind fluctuating load, and torque) are obtained using a direct integration method. Fluctuating wind pressure and the corresponding integration length provide the straightfor  
Figure 7: Spectra of typical pressure taps with \(D/B=3\): (**a**) windward side; (**b**) front part of the lateral side; (**c**) rear part of the lateral side; (**d**) leeward side. ward aerodynamic shape of the rectangular prism. The pressure tap layers at the model's bottom (1#), 2/3H (8#), and upper half (11#) were selected to provide the power spectrum functions of the fluctuation aerodynamics of rectangular prisms under various boundary layer turbulence conditions. The along-wind fluctuation load, the across-wind load, and the torque dimensionless power spectra for the rectangular prism with \(D/B=1/3\), are shown in Figures 8 and 9. In these figures, \(S_{D}(f,z)\), \(S_{L}(f,z)\), and \(S_{T}(f,z)\) represent the three component fluctuation aerodynamic spectra; \(\sigma_{D}\), \(\sigma_{L}\), and \(\sigma_{T}\) are the root mean square; \(V_{H}\) is the average velocity at the top of the model. There is substantial consistency in terms of the fluctuating aerodynamic spectrum of rectangular prisms when the width of the windward side is greater than the downstream spreading length (\(D/B<1\)). According to Figures 8a and 9a, the along-wind turbulent component primarily affects the along-wind fluctuating wind load, which is more severely affected in the low frequency range. The across-wind fluctuating wind  
Figure 8: The dimensionless power spectra of fluctuating aerodynamic forces with \(D/B=1/3\) in \(BL1\): (**a**) along-wind fluctuating load; (**b**) across-wind fluctuating load; (**c**) torque. Figure 9: The dimensionless power spectra of fluctuating aerodynamic forces with \(D/B=1/3\) in \(BL2\): (**a**) along-wind fluctuating load; (**b**) across-wind fluctuating load; (**c**) torque. load and torque are largely defined by vortex shedding, and the spectrum contains spectral peaks that are comparable to the characteristics of the fluctuating wind pressure spectrum [2; 3; 4; 9; 13; 14; 19; 25; 28; 33]. The power spectrum is primarily affected by the weakening of the low frequency area. The high-frequency fluctuations are augmented as the wind field turbulence intensity increases, and the energy is distributed over a larger spectral bandwidth. The experimental results further demonstrate the impact of end effects on fluctuating wind loads, with reduced power spectrum values, at roughly 0.12 Hz. The fact that these phenomena are more noticeable in the \(BL1\) suggests that the alteration of turbulence characteristics interferes with vortex shedding and top flow in a significant manner. The fluctuating aerodynamic spectra of the square prism are closer to those of the rectangular prism as they have a small side ratio (\(D/B<1\)), as shown in Figure 10. It should be observed, nonetheless, that the torque also has a smaller spectral peak at \(2f_{s}\), and it is more substantial near the top of the model in \(BL2\). In addition, it also has a significant spectral peak at the vortex shedding frequency, as shown in Figure 10c. This may be occur due to the occasional reattachment of the separated flow that is already present and facilitated by the end effect; however, this study did not adequately document these flow specifics. The power spectra at \(D/B=4\) are shown in Figures 11 and 12, and as the side ratio of the rectangular prism grows (that is, as the downstream spread exceeds the windward width), its fluctuating aerodynamic spectra exhibit distinct characteristics. The results given in the preceding section indicate that for rectangular prisms with large side ratios (\(D/B\geq 2\)), there are notable changes in the fluctuating wind pressure spectra, primarily on the lateral and leeward sides.