# Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms
## 3 Results and Discussion
### Spectral Characteristics of Typical Pressure Taps
The variable wind pressure spectrum for the leeward pressure taps (Figure 5e,f) has a spectral peak at vortex shedding frequency \(f_{s}\), suggesting that vortex shedding regulates the leeward aerodynamic force [3, 6, 7, 8, 13, 19, 20, 25, 35]. It should be noted, however, that the spectral peak lowers as the distance is reduced at the leeward side's midpoint, and the low-frequency value of the peak steadily rises. This suggests that when moving to the middle of the leeward side, the wake vortex is continuously absorbing the low-frequency fluctuation component energy, and the influence of the vortex shedding is gradually waning. Additionally, the asymmetry of vortex shedding may be the reason why the spectrum function towards the leeward side's midpoint has a smaller peak at \(2f_{s}\), and why the turbulence intensities remain close to 30% (Figure 5f). As is evident from Figure 6, a similar technique was used to study the wind pressure spectrum features of rectangular prisms with side ratios of \(D/B=1/2\) and 2. The spectrum  
Figure 5: The spectral density function of the typical pressure taps in the square prism: (**a**) windward side, \(BL1\); (**b**) windward side, \(BL2\); (**c**) lateral side, \(BL1\); (**d**) lateral side, \(BL2\); (**e**) leeward side, \(BL1\); (**f**) leeward side, \(BL2\). properties of the fluctuating wind pressure are compatible with a square prism when the wide side is upwind (\(D/B=1/2\)), as illustrated in Figure 6a,c,e. This suggests that under these operating conditions, the rectangular section's fluctuating wind pressure production and energy transfer mechanisms are similar to those of the square prism [3; 8; 14; 28]. As shown in Figure 6b,d,f, when the narrow side is facing the wind (\(D/B=2\)), it is possible for the separated shear flow to reattach under conditions of high-level turbulence intensity, which would significantly alter the spectrum features. The turbulent flow disturbance increases the separation shear flow's coiling influence on the free mean fluid in the return zone as the pressure tap moves away from the separation point. The fluctuating wind pressure energy is transported from the peak frequency to a larger spectral bandwidth  
Figure 6: Spectra of typical pressure taps with \(D/B=2\) and \(1/2\): (**a**) windward side, \(D/B=1/2\); (**b**) windward side, \(D/B=2\); (**c**) lateral side, \(D/B=1/2\); (**d**) lateral side, \(D/B=2\); (**e**) leeward side, \(D/B=1/2\); (**f**) leeward side, \(D/B=2\). as a result of the interference between the turbulent components, separated and reattached flows, various scale vortices, and the frequent energy exchange. The reattachment flow may divide once more when the pressure taps near the tail of the lateral side exhibit the spectral peak of the vortex shedding feature; despite this, the high-frequency value of the fluctuating pressure spectrum in this area still increases. Overall, the interference of the separated shear flow reattachment, and the entering turbulence, changes the fluctuating pressure spectrum features, similarly to those under vortex shedding control. Studies in this field have shown that the separated shear flow will reattach on the lateral side, whereas the comparable side ratio in the uniform flow is approximately \(D/B=2.8\)[19; 30; 35; 36]. However, the incoming turbulent flow disturbances increase the curvature of the separation shear layer, further compressing the size of the primary vortex in the separation zone; this causes the reattachment phenomena to manifest earlier, at smaller side ratios, such as \(D/B=2\) in the current study. The larger-scale vortices in the shear flow are quickly broken into smaller-scale vortices as a result of the lateral sides' stretching, squeezing, and dragging effects on the vortices. This results in spectral characteristics that differ from those controlled by vortex shedding.