## 4 Results and Discussion
### Flow Induced Vibration of Two Staggered Cylinders
#### 4.2.3 Wake Vortex Structure
The fluid-structure interaction between the downstream cylinder and fluid was enhanced, the FIV of the downstream cylinder was strengthened, and its amplitude also increased. As shown in Figure 13e, when the reduced velocity increased to 12, the vortex shedding mode behind the downstream cylinder could be observed to change from P and S to S, and the wake region behind the cylinder became narrow and slender. As a result, the pressure fluctuation in the wake region decreased, the FIV of the downstream cylinder was weakened, and its amplitude also decreased. At \(T=0.6D\), the wake vortex structure of two cylinders with roughness strips at different reduced velocities is depicted in Figure 14. From Figure 14a-c, it can be clearly seen that the vortex shedding mode of the downstream cylinder changed from S to P and finally to P and S, and the upstream cylinder shedding mode changed from S to P. During this period, the number of vortex shedding increased and the pressure fluctuations in the wake area increased. Due to the influence of upstream vortex shedding, the fluid-solid interaction between the downstream cylinder and fluid was promoted, and the vibration of the downstream cylinder was strengthened. It can be observed from Figure 14d, e that the wake of the upstream cylinder became longer at a high reduced velocity. At this time, besides the inflow velocity, the downstream cylinder was the main factor affecting the upstream cylinder vibration. Figure 12: The wake vortex structure of two cylinders with roughness strips at different reduced velocities at \(T=0\). Figure 13: The wake vortex structure of two cylinders with roughness strips at different reduced velocities at \(T=0.4D\). In the classical FIV of a single cylinder, when the reduced velocity is greater than 11, the vibration of the cylinder is in the lower part of the support, and the amplitude of the cylinder is very small; however, the existence of the downstream cylinder makes the boundary layer of the upstream cylinder separate ahead of time, and the upstream cylinder vibration maintains at a higher amplitude. The gap flow between two cylinders promotes the upstream cylinder vibration and suppresses the downstream cylinder vibration. The vortex shedding mode of the downstream cylinder could be approximately regarded as S at the far wake. Figure 15 shows the wake vortex structure of two cylinders with roughness strips at different reduced velocities at \(T=1.0D\). This was similar to the vortex shedding mode at \(T=0.6D\). This is because the two cylinders were located in the dominant area of the gap flow when \(U^{*}<8\), \(1.0D\geq T\)\(\geq 0.6D\). When the distance was small, the staggered distance had little effect on the vibration of two cylinders. For \(U^{*}=9\), the upstream cylinder shed in the P mode, and the downstream cylinder shed along with the upstream cylinder shedding in near wake, thus presenting a P and S mode, which lasted only for a short time and finally became the S mode, as shown in Figure 15c. From Figure 15d, e, it can be seen that when the reduced velocity increased to a critical value, the gap flow between the upstream cylinder and the downstream cylinder changed from a complete vortex to a fine flow, resulting in a narrow near wake of the downstream cylinder, a smaller pressure fluctuation in the wake region, and a suppression of its vibration.