# Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms
## 3 Results and Discussion
### Spectral Characteristics of Fluctuating Aerodynamic Forces
The spectral properties of the torque and across-wind fluctuating wind load are mainly impacted by the aforementioned variances. When the side ratio \(D/B\) hits 2, the separated shear flow reattaches to the lateral sides under the effects of turbulent flow, resulting in a reduced spectral peak and an increase in the spectral bandwidth. However, with various turbulent entering flows, there are differences in variation tendencies. Although the fixed value of \(BL2\) is reached earlier, at \(D/B=2\), for \(BL1\), the bandwidth of the across-wind fluctuating wind load and torque spectrum is essentially fixed until \(D/B\) reaches 3. This finding suggests that one of the key elements contributing to the separated shear flow's early reattachment is the increased turbulence intensity of the wind field [6; 7; 8; 9; 16; 18; 19; 20; 21; 24; 25]. Additionally, when the separated flow reattachment takes place on the lateral side, the across-wind fluctuating wind load spectra  
Figure 10: The dimensionless power spectra of fluctuating aerodynamic forces on the square prism in \(BL2\): (**a**) along-wind fluctuating load; (**b**) across-wind fluctuating load; (**c**) torque. display a lower spectral peak that is close to the approximate frequency of 0.2. This spectral peak could be the result of a subsequent shedding of the reattached separating shear layer at the back of the lateral side, which would produce the signature wake turbulence. When the turbulence intensity rises, the across-wind fluctuating wind load spectrum's bandwidth expands noticeably, and the value of the second peak falls. This demonstrates that the disturbance effect of the higher turbulence intensity is enhanced, and different kinds of small-scale vortices continuously dissipate as they move downstream. The across-wind fluctuating wind load spectra in the vertical direction are more similar at low frequencies, but the second spectral peak (towards the top) is higher because of the presence of a non-negligible end effect. In general, the power spectrum parameters for the torque of rectangular prisms are more akin to those of across-wind fluctuating wind loads. Torque-related studies are still comparatively scarce and still not fully understood because of the complicated aerodynamic mechanism underlying torque. Figure 11: The dimensionless power spectra of fluctuating aerodynamic forces with \(D/B=4\) in \(BL1\): (**a**) along-wind fluctuating load; (**b**) across-wind fluctuating load; (**c**) torque. Figure 12: The dimensionless spectral functions of fluctuating aerodynamic forces with \(D/B=4\) in \(BL2\): (**a**) along-wind fluctuating load; (**b**) across-wind fluctuating load; (**c**) torque. In this section, the fluctuating aerodynamic forces and spectrum characteristics of rectangular prisms are analyzed based on experimental results, and the role of influencing factors such as turbulence parameters, side ratios, end effects, and various flow phenomena are discussed. Overall, the along-wind fluctuating wind load of the rectangular prism is mainly controlled by incoming turbulence, and its power spectrum is proportional to the along-wind fluctuating velocity spectrum. The aerodynamic mechanisms of the across-wind fluctuating load and torque are more complex, and the turbulent boundary layer flow, side ratio, vortex shedding, separation and reattachment flow, and end effects all have important effects on these mechanisms. However, it is not yet possible to fully understand how large-scale turbulence interferes with the separation flow, the change in the size of the separation bubble, the location of the reattachment point and secondary separation point, and how the vortices move on different scales, among other phenomena. At the same time, due to the limitations of the experimental methodology employed, this study has not yet been able to fully reveal the specific roles of the influencing factors, and the cross-correlations between the factors and their combined effects could not be explored in depth.