# Wind Forces and Flow Patterns of Three Tandem Prisms with a Small Height-Width Ratio
## 3 Results and Discussions
### Dependency of Wind Force Coefficients on Prism Spacing  
This section analyzes the interference effects of the clear spacing on the wind force coefficients of the three tandem prisms. The mean and RMS coefficients of wind forces were calculated from the 90 s duration pressure time histories in wind tunnel tests. To quantitatively evaluate interference effects on wind forces, interference factors (_IF_) of drag and roof uplift coefficients are defined as Equations (5) and (6), respectively. Since the magnitude of the lateral lift coefficient of the isolated prism is close to zero, the lateral lift coefficients of prisms are not expressed in the form of interference factors to avoid being divided by zero. \[IF_{C_{D}}=C_{D,\;disturbed}/C_{D,\;isolated} \tag{5}\]  
\[IF_{C_{RL}}=C_{RL,\;disturbed}/C_{RL,\;isolated} \tag{6}\]  
where the numerator and denominator are the wind force coefficients of the disturbed prism and isolated prism, respectively. Figure 7 shows the variation of coefficients of mean wind forces and RMS wind forces of three tandem prisms with the spacing ratio (_S_/W). As shown in Figure 7, the wind force coefficients of tandem prisms with _S_/W in previous studies [2; 13; 22] are compared with those in this present study. The displayed previous results include mean and RMS drag coefficients of the downstream prism with _H_/_W_ = 3 in Sakamoto and Haniu [2], mean and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mean \(C_{D}\)** & **RMS \(C_{D}\)** & **Mean \(C_{LL}\)** & **RMS \(C_{LL}\)** & **Mean \(C_{RL}\)** & **RMS \(C_{RL}\)** \\ \hline
0.73 & 0.14 & 0.01 & 0.07 & 0.35 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Wind force coefficients of the isolated prism. Figure 6: Pressure coefficients of the isolate prism: (**a**) Mean pressure coefficients; (**b**) RMS pressure coefficients. RMS drag coefficients of the downstream 2D square prism in [PERSON] et al. [22], and coefficients of mean drag and mean roof uplift of the downstream prism with \(H\)/\(W\) = 0.5 immersed in a large group of prisms in [PERSON] and [PERSON] [13], where the RMS wind force coefficients were not discussed. It can be found that the mean and RMS coefficients of the drag and roof uplift of the upstream prism A are not sensitive to the variation of the spacing, and their values are close to those of the isolated prism. As shown in Figure 7, when spacing ratios are \(S\)/\(W\)\(\leq\) 0.4, shielding effects among prisms are significant, which makes interference factors of mean drag coefficients of downstream prisms B and C very small, and these are similar to results in [13]. According to the flow patterns demonstrated in [PERSON] et al. [23], this flow pattern among prisms at \(S\)/\(W\)\(\leq\) 0.4 is regarded as the skimming flow regime. In addition, for the two tandem prisms with \(H\)/\(W\) = 3 [2], the negative mean drag coefficients of the downstream prism were observed at small spacing ratios (Figure 7a). This phenomenon is not found among the tandem prisms with \(H\)/\(W\) = 0.4 in this present study. At spacing ratios \(S\)/\(W\)\(\leq\) 0.4, the  
Figure 7: Interfered wind forces of three tandem prisms: (**a**) Interference factors of drag coefficients; (**b**) Interference factors of roof uplift coefficients; (**c**) Lateral lift coefficients. other wind force coefficients of downstream prisms except for the mean lateral lift are small compared with those of the isolated prism. It is interesting to note from Figure 7 that when the spacing ratios are \(0.4<S/W\leq 0.8\), the mean and RMS interference factors of drag and lateral lift of the downstream prisms B and C have large local peaks, increase and decrease rapidly in this prism spacing range, and then increase with the increase of the prism spacing at \(S/W>0.8\). The RMS \(IF_{C_{RL}}\) of downstream prisms and mean \(IF_{C_{LL}}\) and RMS \(IF_{C_{LL}}\) of prism A also have similar variations at \(0.4<S/W\leq 0.8\), and the mean \(IF_{C_{RL}}\) reaches the local maximum at \(S/W=0.7\).