## 1 Introduction  
Fluid flow around a cylinder is a universal phenomenon in engineering practice, i.e., heat exchanger tubes, marine cables, high-rises, and civil engineering structures. Vortex shedding behind bluff cylinders is the cause of vortex-induced vibration (VIV) which can result in structural damage under certain unfavorable conditions. In addition, there have been a variety of investigations about vortex-induced vibration from different perspectives in recent years [1, 2]. Eliminating the alternating shedding vortices in the cylinder wake and suppressing the cylinder vibration are of important significance. Fluid has a huge influence on bluff body structures, and there are many relative research [3, 4, 5]. Studies on flow control of bluff body have specified a new orientation for the flow control problems, and they have gained more and more concerns in recent years. Controlling methods can be mainly divided into two types: passive control and active control. Passive flow control could change the flow conditions to achieve the goal of flow control without consuming any external energy [6, 7, 8, 9, 10]. Another flow control method is active flow control, which requires external energy infused into the flow field. Moreover, active flow control could introduce the proper perturbation to change the inner flow mode. Several active flow control methods have been investigated to suppress vibration as well as improve aerodynamic performance, i.e., drag reduction, using wall vibration [11; 12], suction and injection [13; 14; 15; 16], momentum injection [17; 18; 19; 20], bionic control method of traveling wave wall, etc. The TWW is one of the bionic based flow control methods and it has been developing rapidly in recent years. The boundary layer near the rigid wall comes into existence when the viscous fluid flows pass the wall. However, making the cylinder surface to be flexible or movable may help to weaken the boundary layer. The \"fluid roller bearing\" (FRB) effects of the axisymmetric TWW was used by [PERSON] and [PERSON] [21] to sharp into a series of vortex rings. The main flow was separated from the near-wall flow accompanied by friction drag and pressure drag significantly reduced. [PERSON] et al. [22] carried out a numerical simulation to find out the proper parameter (wave amplitude, wavelength and ratio of wave velocity to incoming velocity) for the FRB effects on infinite and finite two-dimensional TWW. Large flow separation was eliminated after applying TWW on airfoils, and the vortex shedding of streamline airfoils with a large wind attack angle was restrained to provide more lift. [PERSON] et al. [23] proposed a transverse traveling wave (TTW) control method to manipulate the unsteady flow around a circular cylinder at Re = 500. A fluid FRB was introduced in this method, and the vortex shedding was eliminated because the global flow remained attached to the surface. [PERSON] et al. [24] simulated the rear section of a cylinder with TWW, and the cylinder was elastically mounted with two degrees of freedom. The simulation took fixed wave amplitude, wave number and ratio of wave velocity to incoming velocity. In addition, the whole process was completely simulated starting with flow around the fixed cylinder, to the oscillating cylinder, and finally to the oscillating cylinder with TWW. In the present paper, TWW was placed on the rear section of a fixed cylinder, and the CFD numerical simulation was adapted to investigate the influencing factors for suppressing the cylinder oscillating wake. The TWW was activated when the alternating shedding vortex behind the fixed circular could be stably observed in the present numerical simulation. There are several steps we need to comply with as per control variate technique. Firstly, fixed velocity ratio and maximum wave amplitude were used to measure the control effect of four kinds of TWW propagation direction for suppressing the oscillating wake.