## 4 Results and Discussion
### Vortex Shedding Frequencies  
Figure 19 presents the lift coefficients power spectral density of three cylinders at various \(L/D\), respectively. The Strouhal number \(St\) is defined as \(fD/U_{0}\). At \(L/D=1.1\), the spectra of downstream cylinders are broad-banded. A dominant frequency of \(St=0.053\) can be identified for the three cylinders. In addition, a second harmonic frequency of \(St=0.701\) occurs. It can be attributed to the interactions of shear layers generated at cylinder A with those from the front side of cylinders B and C. The existence of a second harmonic frequency at low \(L/D\) at \(Re=3\times 10^{6}\) is consistent with that for low Reynolds numbers (\(100-300\)) by [PERSON] et al. [21]. At \(L/D=1.2,1.3\), only one spectral peak is identified in the upstream cylinder, \(St=0.67\) and \(St=0.425\), respectively. While downstream cylinders' power spectral density has multiple peaks and the corresponding power of these peaks are at similar values, illustrating that drastic vortex interaction exists. In contrast to the biased-gap flow pattern found for two cylinders placed side by side [7], which led to the observation that a wider wake cylinder has a lower vortex shedding frequency than the narrow wake cylinder, the dominate frequency of the two cylinders with either wide or narrow wake has the same value. This could be because of the presence of cylinder A. As \(L/D\) increases to 1.4, dominant frequency, \(St=0.319\), occurs at the downstream cylinders. This implies that the interaction between the shedding processes weakens as the gap space is greater. However, as displayed in Figure 7e,f, the gap flow at \(L/D=1.4\) still has a tendency of bias towards cylinder C. It demonstrates that \(L/D=1.4\) is a critical spacing ratio from deflected gap flow to anti-phase flow. As \(L/D\) increases, the \(St\) of all cylinders gradually approach that of the flow past a single cylinder. When \(L/D=3.5\), all cylinders have the same frequency (\(St=0.383\)), which is equivalent to that of a single cylinder. This indicates that the disturbance becomes very weak and that each vortex shedding behind every cylinder behaves like the flow past a single cylinder. Furthermore, it is notable to highlight that the power density is much higher at the dominant frequency when \(L/D=2.5\). This implies that the vortex shedding  
Figure 18: Power spectral density (PSD) of \(Cl\) of each cylinder at different \(L/D\). at these frequency is pronounced. This observation is in accordance with the discontinuous jump in \(\bar{Cd}\), \(Cd^{\prime}\), and \(Cl^{\prime}\) mentioned in the previous section, as shown in Figure 15.  
The fluctuation of \(St\) with \(L/D\) is seen in Figure 13. As for the situations with multi-peak spectral densities, the frequency with the largest power density is collected. It is worth noting that cylinders B and C have the same dominant frequency at all \(L/D\); nevertheless, only one set of data is shown for clarity. The \(St\) of three cylinders is equal in single bluff body flow, in-phase flow, and co-shedding flow. It reaches the minimum value at \(L/D=1.1\). In the in-phase flow regime, the value of \(St\) is 0.340, which is 88.7% of that for a single cylinder. In the co-shedding flow regime, \(St\) equals that for a single cylinder, demonstrating that \(L/D=3.5\) is a crucial spacing ratio of the two flow regimes. Figure 20 presents the time-averaged pressure distributions of the three cylinders in different flow regimes, where the pressure distribution \(C_{p}\) is defined as \(C_{p}=(\bar{p}-p_{\infty})/(0.5\rho U_{0}^{2})\), in which \(\bar{p}\) is the time-averaged local static pressure on the cylinder and \(p_{\infty}\) is the reference pressure. For description convenience, some special parameters, \(C_{pst1}\), \(C_{pst2}\), \(C_{pb}\), \(C_{pm1}\), and \(C_{pm2}\) are defined first, as shown in Figure 21. \(C_{pst1}\) and \(C_{pst2}\) are the pressure coefficients at the upper and lower stagnation points, \(\theta_{pst1}\) and \(\theta_{pst2}\), respectively.