# Spectral Characteristics of Fluctuating Aerodynamic Forces Acting on Rectangular Prisms
## 2 Experimental Setup  
The experiments were conducted in a closed-circuit wind tunnel, with a test section of 22.5 m (width) \(\times\) 4.5 m (height) \(\times\) 36 m (length), as shown in Figure 1. The models were designed to be rigid, and the height of all the models was 1.6 m. The narrow sides of all models were of an identical width, at 100 mm, and the lengths of the other sides varied between 100 mm, 200 mm, 300 mm, and 400 mm, respectively. Therefore, with the 4 models positioned at wind directions of 0\({}^{\circ}\) and 90\({}^{\circ}\), one comprised rectangular prisms with seven different side ratios in total (i.e., \(D/B\) = 1/4, 1/3, 1/2, 1, 2, 3, and 4). The models were made of transparent Perspex with severed transverse ribs to increase its stiffness. A total of 336 pressure taps were installed on the square model, and 624 pressure taps were installed on each rectangular model. The taps were uniformly distributed across 12 levels (Nos. 1\(\mu\) to 12\(\mu\)), as illustrated in Figure 2.  
DSM3400 scanners with an acquisition accuracy of \(\pm\)0.1% were installed inside each model, and they were used to simultaneously monitor surface pressures [6; 11; 14; 19; 31]. Data length can be used to satisfy the needs of spectral characterization, with a data sampling time of 120 s, and an acquisition frequency of 256 Hz. Direct pressure integration, for each pressure tap and their integral lengths, was used to determine the aerodynamic force of each layer.  
Figure 1: A rectangular prism installed in wind tunnel.  
Figure 2: Layout of pressure taps. (unit: mm).  
The boundary layer turbulence flows were simulated using the traditional passive method, which involves arranging upstream spires and the surface roughness on the wind tunnel floor. For comparison, all tests were performed on two types of atmospheric boundary layer, named _BL1_ and _BL2_ flows, which represent the ground categories of open country and urban terrain (GB 50009-2012, Architectural Industry Press of China [32]), respectively. The measured mean wind velocity (\(U_{z}\)) and turbulence intensities (\(I_{u}\)) are shown in Figure 3, where \(z_{0}\) is the reference height of the wind profile, \(z_{0}=1.9\) m; \(U_{0}\) is the reference mean velocity; and \(z_{z}\) is the test height. The reference height of the pressure test was set at 3/4H of the model, that is, \(z=1.2\) m, and the corresponding wind speed was approximately 9.6 m/s. The Reynolds number obtained from the test wind velocity and the rectangular model feature size was approximately 1.15 \(\times\) 10\({}^{5}\), and its effect was ignored. The dimensionless power spectra of the turbulent fluctuation components in the along-wind and across-wind directions are shown in Figure 4. It is evident that the simulated boundary layer's turbulent flows can be fitted well using von-Karman's spectrum, and the integral length scale may be calculated by fitting this spectral model in the range of 1.1-1.42, which is basically consistent with the natural shear flows. The characteristic parameters of two turbulence fields are shown in Table 1.  
Figure 4: Normalized wind spectra at \(z=1.2\) m: (**a**) along-wind velocity component; (**b**) across-wind velocity component.  
Figure 3: Mean wind and turbulence intensity profile.