###### Abstract  
The vortex-induced vibration of a circular cylinder and two inline circular cylinders near a plane wall at a Reynolds number of 150 is numerically investigated by using a self-developed immersed boundary method called the local domain-free discretization (DFD) method. The cylinders are elastically mounted with a mass ratio of \(8/\pi\) and a 0 damping ratio and can only vibrate in the transverse direction. The reduced velocity varies from 2 to 9, with an interval of 1. Three gaps, \(e=0.1D\), \(1D\), and \(2D\) (\(D\) is the cylinder diameter), are investigated for the case of an isolated cylinder and two inline cylinders while the center-to-center spacing (\(L\)) is \(1.5D\) for the two-inline-cylinders case. A model for the collision of the cylinders with the wall is adopted in which the bouncing back is forced when the gap between the cylinder and the plane wall is smaller than \(0.02D\). It is observed that the existence of the plane wall significantly affects the cylinder response both in the one-isolated-cylinder and two-inline-cylinders cases. The features, including vibration amplitudes, frequencies, fluid forces, the maximal or minimal gap between the cylinder bottom and the plane wall, and the vortex shedding patterns, are explored in detail. Interactions between the front and rear cylinders and differences between the one-isolated-cylinder and two-inline-cylinders cases are discussed. The research has immense significance for the design of near-wall cylindrical structures, such as the deep-water pipeline system on the seafloor. v Article  
2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 2024 15 November 2024 15 November 2024 2024 15 and \(D\) is the cylinder diameter) [3]. [PERSON] and [PERSON] [7] categorized the cylinder response into two types based on the magnitude of \(m^{*}\zeta\). For a low \(m^{*}\zeta\), the response curve has three branches when plotted versus \(U_{r}\), named the 'initial', 'upper', and 'lower' branches. However, for a high \(m^{*}\zeta\), the 'upper' one does not exist anymore. There are many vortex shedding flow patterns in the cylinder wake region, such as '2S' (two single vortices formed per cycle), '2P' (two pairs of vortices formed per cycle), and '2T' (two triplets of vortices per cycle). Various response branches may be associated with vortex shedding mode characteristics. Earlier research revealed that the initial branch corresponds to the '2S' mode while a '2P' mode appears in the upper and lower branches [8; 9]. In engineering practices, near-wall cylindrical structures are commonly encountered. For example, the deep-water pipeline system traversing over the seafloor (Figure 1a,b) or the flat-bottomed ground-supported silos used for storing granular-like material (Figure 1c). These cylindrical structures may suffer from fluid dynamics and can develop different buckling modes [10], including elephant foot buckling [11], top-of-wall damage buckling [12], and elastic buckling [13]. These can all be regarded as near-wall cylinders. In this paper, the VIV of the rigid cylindrical structures near a plane wall is considered, which is often seen in the deep-water pipeline system (Figure 1a,b). Compared to the case of a wall-free cylinder, the flow behind the near-wall cylinder will become much more complex due to the interactions between the wall boundary layer and the shear layer over the cylinder. In the VIV of the near-wall cylinder, the gap ratio \(e/D\) (\(e\) the gap between the bottom of the cylinder and the wall) is a crucial parameter. A few recent studies have been focused on the VIV of a circular cylinder close to a plane boundary. [PERSON] et al. [14] conducted a numerical study on the wall effects at \(Re=100\) for \(0.5\leq e/D\leq 10\) and they found that the lock-in region became larger for a lower \(e/D\).