## 4 Results and Discussion
### Flow Patterns
#### Deflected gap flow  
As \(L/D\) increases to 1.2-1.4, the gap flow is deflected towards one of the downstream cylinders and forms a deflected gap flow pattern. At \(L/D=1.2\) and 1.4, gap flow is deflected towards the downstream cylinder C and produces a narrow wake behind it, and the opposite when \(L/D=1.3\). Different computation procedures produce random deflection directions. A switch in the directions of the gap flow is not found throughout the computation process, which is consistent with the findings by [PERSON] [16] and [PERSON] [21]. As regards double cylinders arranged side by side, nevertheless, [PERSON] [52] and [PERSON] et al. [53] found a shift in the deflection direction of the gap flow. The existence of the upstream cylinder might limit the direction change of the deflection flow. Figure 7 demonstrates that the vortex shedding of the downstream cylinder with the gap flow bias is suppressed. The suppression lessens with the increase of \(L/D\). From the time-mean streamlines in Figure 7b,d,f, it is observed that the recirculating bubble of the wider wake downstream cylinder is longer and broader. The cylinder with a wide wake has a lower drag coefficient compared to the cylinder with narrow wake, which is consistent with the biased gap flow of the two cylinders arranged side by side [7]. Figure 6: (**a**) Normalized spanwise vorticity \(\omega_{z}D/U\); (**b**) time-averaged streamlines in the plane \(z=2\) D at \(L/D=1.1\). As \(L/D\) increases, the flow pattern becomes anti-phase flow. Anti-phase is referred to the occurrence of 180\({}^{\circ}\) phase lag in the time history of lift forces between the downstream cylinders. Figure 11 presents the relationship of the phase lag \(\phi\) of the downstream cylinders with \(L/D\), which is obtained through the FFT analysis of the \(Cl\) of two downstream cylinders. Since there is no significant principal frequency of \(Cl\) of the downstream cylinder when \(L/D<1.4\), their phase lag data are not shown in the figure. In the anti-phase flow regime, the vortices on the free-flow-side of the downstream cylinder shed simultaneously and are symmetrical relative to the wake center line. The shear layers of the upstream cylinder appear to roll up and produce vortex shedding, with a weaker intensity compared with the downstream cylinders. They are elongated at the gap, and finally pair with the the vortices produced by gap-side downstream cylinders and blend in with the wake flow. The size of the recirculation zone of the upstream cylinder is way smaller than that of the downstream cylinders, as seen in Figure 8d. Figure 8: Normalized spanwise vorticity \(\omega_{z}D/U\) in the plane \(z=2\) D at: (**a**) \(L/D=1.5\); (**b**) \(L/D=1.7\); (**c**) \(L/D=2\); (**d**) time-averaged streamlines at \(L/D=1.7\). Figure 7: Normalized spanwise vorticity \(\omega_{z}D/U\) and time-averaged streamlines in the plane \(z=2\) D at: (**a**,**b**) \(L/D=1.2\); (**c**,**d**) \(L/D=1.3\); (**e**,**f**) \(L/D=1.4\). Figure 9a-c shows the vorticity contours at \(L/D=2.3,2.5,3\). The flow pattern belongs to in-phase flow, because the vortex shedding of the downstream cylinder presents an in-phase fashion. As shown in Figure 11, the phase lag of the two downstream cylinders is near 0 when \(L/D>2\). The vortices from free-flow-side shear layers of the cylinder B and the gap-side shear layers of the cylinder C shed synchronously, which is exactly the opposite for anti-phase flow. The vortex generated from the upstream cylinder is elongated at the gap and interacts with the vortex of the gap-side shear layers of the downstream cylinders. As \(L/D\) increases, the vortices shed by the upstream cylinder show an oscillation in the vertical direction in order to pair with the vortex generated from downstream cylinders. These interactions bring on the dissipation of vortices' energy of the upstream cylinder. Figure 9d only shows the time-averaged streamline for \(L/D=2.5\) because the difference between each \(L/D\) in in-phase flow is insignificant.