## 1 Introduction
In addition, it was found that there were two kinds of vortex shedding modes of 2P and 2S (2P is a pattern where, in each complete cycle, a pair of vortexes are shed. 2S is a pattern where, in each complete cycle, a single vortex is shed [16]) at \(U_{r}=U/(\!\!\!f_{n}\). \(D)=7.8\) and \(5000\leq Re\leq 27,000\). [PERSON] et al. [17] observed the flow field structure of two cylinders in tandem arrangement with different spacing ratios and calculated the vorticity lines and the force on the cylinders. The calculation results were basically consistent with the experiment results of [PERSON] [18] and [PERSON] [19]. As \(L/D<3\), the downstream cylinder received a negative effect. On the other hand, as \(L/D\geq 3\), there was a positive influence. In recent years, with the development of technology, [PERSON] et al. [20] presented the flow field of tandem cylinders by the particle image velocimetry (PIV) method. It can be observed that the wake of the upstream cylinder influenced the inflow condition of the downstream cylinder, and the downstream cylinder reacted  
Figure 1: Simplified classification scheme of the flow patterns for two tandem circular cylinders in cross-flow. upon the wake dynamics and the wake vortex region of the upstream cylinder. [PERSON] et al. (2012); [PERSON] et al. (2012) and [PERSON] et al. (2013) determined the separation points of the wake by measuring the pulsating pressure distribution and applying a hot-film sensor on the surface of the cylinder. In later papers, scholars paid more attention to the oscillation interference of two cylinders. [PERSON] et al. (2014) concluded that the wake-induced vibration (WIV) phenomenon of the downstream cylinder was caused by the interaction of the fluid and the unsteady vortex structure between the wakes of the upstream cylinder, as shown in Figure 2. If the unsteady vortices from the wake were removed, WIV would not be excited. The amplitude response of the WIV region decreased as the spacing ratio increased for \(x_{0}/D\geq 4.0\). In the tests, for \(x_{0}/D=20.0\), the amplitude was drastically reduced and closely resembled that of the vortex-induced vibration (VIV) of a single cylinder; the WIV grew weaker as the spacing ratio increased until the interference was irrelevant and the cylinder behaved similar to an isolated body. A favorable phase lag between the displacement and the fluid force guaranteed that the positive energy that was transferred from the flow to the structure sustained the oscillations. [PERSON] et al. (2015, 2016) established a three-dimensional numerical model to analyze the fluid-structure interaction in the tube bundle. The results showed that the lift and amplitude of the downstream tube increased with the increase of the spacing ratio. For \(L/D>2\), the fluid force coefficient and amplitude of the upstream tube were close to those of the single tube. Most of the previous investigations were performed on two cylinders, and the physical experiments and number simulations were focused on the wake, fluid forces on the surface of cylinders, and near-body disturbance of the cylinders, etc. It can be concluded that the mutual disturbance on the amplitude responses of two cylinders was mostly effect by the spacing of the two cylinders, and the wake characteristics of the cylinders were determined by the Reynolds number. Furthermore, the oscillation responses of the downstream cylinder (circular and non-circular) were greatly affected by the gas (water) dynamics and the vortex shedding (2017, 2018). In the past decade, scholars have begun to pay more attention to the mutual disturbance of prisms and energy conversion with different cross-sections (2020, 2019, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2029, 2021).