## 4 Results and Discussion
### Fluid Force Coefficients  
Figure 15a,b shows the mean and fluctuating drag force coefficients of the three cylinders, respectively. When \(L/D=1.1\), the drag forces on the downstream cylinders are identical and significantly greater than on the upstream cylinder. When \(L/D=1.2-1.4\), two distinct drag force coefficients were obtained for downstream cylinders, which suggests that this \(L/D\) belongs to the deflected gap flow regime. As \(L/D\) increases, the drag coefficients for the downstream cylinders remain identical and slowly converge to the drag coefficient for the flow past the single cylinder. It is worth noting that at \(L/D=2.5\), which belongs to the early onset of in-phase flow, the drag coefficient suddenly increases. The \(Cd^{\prime}\) shows similar characteristics with \(Cd\) as shown in Figure 15b. Figure 14: Instantaneous pressure distributions in the middle section (\(z=2\) m) at different flow pattern regimes. Figure 13: Iso-surface of \(Q=1.5\,U_{0}^{2}/D\) colored by dimensionless streamwise velocity \(U/U_{0}\) at different flow pattern regimes. Figure 15c,d presents the mean and fluctuating lift force coefficients for different \(L/D\), respectively. At \(L/D=1.1\), Figure 15c illustrates that there is a strong repulsive force between the two downstream cylinders. It is due to the existence of a pressure difference between the gap side and free-stream side of the downstream cylinders, which can be shown distinctly in pressure distributions in the middle section of Figure 14a. As shown in Figure 14a, in the case of downstream cylinder B, for example, the negative pressure zone on its free-stream side is shifted forward, while the negative pressure zone on its gap side is shifted back, which results in an upward lift force. When \(L/D=1.2\)-1.4, the sum of two downstream cylinders lift force coefficients, which is presented by the green line, is not zero, and the absolute value of the sum lift coefficient decreases with the increase of \(L/D\). The direction of the sum lift coefficient is opposite to the direction the deflected flow is biased towards. When \(L/D>2.3\), there is a weak attractive force between the downstream cylinders. As \(L/D\) goes to 3.5, the lift force coefficients of all cylinders is close to zero, which fits the scenario of a single cylinder. As shown in Figure 15d, similarly to the \(Cd^{\prime}\), the downstream cylinders undergo a higher \(Cl^{\prime}\) than that of the upstream cylinder. At \(L/D=1.1\), \(Cl^{\prime}\) of the downstream cylinder reaches a maximum. At \(L/D=1.2\)-1.4, the downstream cylinder with a wider wake has a larger \(Cl^{\prime}\). As \(L/D\) increases, \(Cl^{\prime}\) of the downstream cylinders decreases. Similarly to the \(Cd\) and \(Cd^{\prime}\) distributions, \(Cl^{\prime}\) of the three cylinders increases abruptly at \(L/D=2.5\) and then decreases gradually back to be consistent with that of a single cylinder. We regarded that the special phase lag between all three cylinders at \(L/D=2.5\) causes the higher \(\bar{Cd}\), \(Cd^{\prime}\), and \(Cl^{\prime}\). A phase lag of \(0\pi\) occurring at the early period of the in-phase flow regime enriches the shedding of vortices. The observation of fluid coefficients suggests that the interactions among the three cylinders is apparently strong at single bluff body flow, deflected gap flow, and the start of in-phase flow. Figure 15: Variations of mean force coefficients and fluctuating force coefficients with different \(L/D\): **(a)** time mean drag force coefficients; **(b)** fluctuating drag force coefficients; **(c)** time mean of lift force coefficients, green line means the sum of two downstream cylinders; **(d)** fluctuating lift force coefficients. Figures 16 and 17 show the time history curves of \(Cd\) and \(Cl\) at several critical \(L/D\)s for each flow pattern, respectively. It can be seen that the values of both drag and lift fluctuations for the upstream cylinder are smaller than those for the downstream cylinders.