## 1 Introduction  
Ocean current energy is a new type of sustainable energy with huge reserves. With the gradual development of ocean energy and the continuous development of flow-induced motion (FIM), more scholars are focusing on exploiting ocean current energy by means of the FIM phenomenon [1, 2]. A lot of research has been conducted on oscillation characteristics and energy conversion of FIM for a single oscillator or multi-oscillators, and most research has concentrated on circular cylinders. Previously, research methods were mostly experimental studies which were mainly focused on the variation of oscillation characteristics and wakes with spacing, as well as the correlation between Reynolds number and oscillation characteristics of FIM [3]. [PERSON] et al. [4] conducted a series of FIM experiments on two cylinders coupled and uncoupled in tandem with a spacing ratio of \(0.25\leq\) \(L\)/D \(\leq\) 6, and complex mutual interactions were observed between the flow and wake. As oscillation occurred in the crossflow direction, the Reynolds number must exceed 100. It can be concluded that the amplitude of the downstream uncoupled cylinder was strongly influenced by the vortices shed from the upstream cylinder and the spacing ratio. For \(L\)/D \(>\) 3, the wake of the upstream cylinder had a positive effect on the oscillation of the downstream cylinder. Considering the interference of the cylinders, [PERSON] [5; 6; 7] and [PERSON] et al. [8] concluded three wake interference regions, as shown in Figure 1. For the regime between the two cylinders, the wake vortex of the upstream cylinder was attached to the downstream cylinder, the two cylinders almost acted as a single structure, and the two cylinders were similar to a single cylinder and a joint vortex, the so-called extended-body regime (\(1\leq L/D\leq 2\)). For \(2\leq L/D\leq 5\), mutual interference occurred between two cylinders in this range. The distance between the downstream cylinder and the upstream cylinder was smaller than the vortex distance of the upstream cylinder. The vortex wake of the upstream cylinder was attached to the downstream cylinder before the vortex was completely formed, and the downstream cylinder had an effect on the formation of the wake of the upstream cylinder, the so-called reattachment regime. For \(L/D\geq 5\), the two cylinders were vortexed in the co-shedding regime. Subsequently, scholars began to pay more attention to the effect of spacing and the Reynolds number on oscillation. [PERSON] et al. [9] defined and analyzed the wake path with different spacing ratios based on the oscillation wake of the upstream and downstream cylinders for a Reynolds number of \(8.7\times 10^{3}\leq Re\leq 5.2\times 10^{4}\) and spacing ratios of \(1.03\leq L/D\leq 5\). [PERSON] et al. [10; 11] presented a series of physical experiments for the fluid-dynamic instability of a smooth circular cylinder that freely oscillated with linear springs in the wake of an identical stationary cylinder. The results showed that the wake of the upstream cylinder was affected by the amplitude of the downstream cylinder and functioned through the static forces on the downstream cylinder with its proximity to a fixed identical body. [PERSON] et al. [12] concluded that the cylinder oscillation not only affected the lift coefficient and the steady-state drag coefficient but also influenced the mutual interference between the two cylinders at \(4.5\times 10^{4}\leq Re\leq 5.8\times 10^{5}\) and \(2.5\leq L/D\leq 5.02\). [PERSON] et al. [13; 14] found that the interacting wake vortices exhibited different wake patterns for different phase angles in the resonance region by an experimental method used to study the wake of tandem and two parallel cylinders. [PERSON] and [PERSON] [15] found that the resonance region of the tandem cylinders was larger than that of the isolated cylinder, and the region decreased as the spacing ratio \(L/D\) increased.