## 1 Introduction  
Marine structures including oil containment booms, floating tunnel, pipelines and fish-farming float collars cannot avoid the effects of an oscillatory flow derived from the wave and relative structure motions. These marine structures can be viewed as a semi-submerged cylinder under oscillatory flow. The surface distortion and water fragmentation will result in a complicated response and hydrodynamic loads. This problem is still not fully understood and threatens the safety of the relevant marine structures. Thus, it is essential to study the hydrodynamic features of semi-submerged cylinder in an oscillatory flow for the marine structures design. The current research of flow past a cylinder contains mainly three categories including cylinders submerged in infinite depth water, cylinders near the free surface and cylinders partially submerged under the water surface. In the oscillatory flow, many focuses are on the problem of flow past a fully immersed cylinder with infinite depth. [PERSON] et al., (1953) [1]; [PERSON] et al., (1950) [2] first raised a formula to calculate the in-line (IL) component of hydrodynamic force, which is now known as the Morison formula. The drag coefficient (\(C_{D}\)) and added mass coefficient (\(C_{m}\)) in the Morison formula were found to be respectively of value 1.7 and 0.4 through an experimental study of stationary rigid cylinders under wave actions. The values of \(C_{D}\) and \(C_{m}\) for a cylinder under the action of waves were further determined by [PERSON] (1958) [3] through Fourier analysis and it was found that the Stokes parameters have a significant influence on these coefficients. [PERSON] (1973) [4] measured the force in the transverse direction, drag force and added-mass force (inertia) of the fully immersed cylinder in the oscillatory flow. The drag coefficient and added mass coefficient were witnessed to have good agreements with results of [PERSON] (1958) [3]. [PERSON] (1989) [5] and [PERSON] (2006) [6] experimentally studied the effects of the Re number at low Keulegan-Carpenter (KC) numbers on a rigid stationary cylinder under this oscillatory flow. Moreover, [PERSON] (1976) [7] carried out a more comprehensive experimental studies on the forces of cylinders under oscillatory flows in sinusoidal form that was generated through an oscillatory U-shaped tube. The results were systematically reported that the hydrodynamic coefficients closely related with the Re number, Keulegan-Carpenter (KC) number and the relative roughness of the cylinder surface. Moreover, [PERSON] (1985) [8] and [PERSON] and [PERSON] (1990) [9] conducted a comprehensive flow visualization of the flow past cylinder, which provided a better understanding of the underlying fluid mechanism. Therefore, the investigation of hydrodynamic loads on the fully immersed cylinder with infinite depth in an oscillatory flow is relatively comprehensive. Different from flow past the fully submerged cylinder with infinite depth, there are few studies focusing on cylinders near the free surface and cylinders partially submerged below the water surface in an oscillatory flow. As for close to free surface cylinders, the existing research mainly focuses on the steady flow field. [PERSON] (1975) [10] investigated the drag and transverse forces and discussed the relationships of the drag force and the lift force respectively with a submerged gap ratio. [PERSON] and [PERSON] (1978) [11] further observed that the free surface can greatly influence the response frequency and the corresponding Strouhal number decreases quickly with the submerged gap ratio decreasing. [PERSON] et al. (1999) [12] experimentally investigated a cylinder under steady flow and highlighted the strong effects of the boundary layer development on this lift force. Different from the experimental studies, computational fluid dynamics (CFD) provides more opportunities to perform comprehensive studies on the underlying mechanisms of complicated fluid-structure interactions (FSI) problems. [PERSON] et al. (1997) [13] and [PERSON] et al.