Numerical investigation of vortex induced vibration of a circular cylinder of low dimensionless mass $(m^{*}=1,2)$ near a rigid wall is carried at a Reynolds number $Re=300$ for a wide range of reduced velocity, $2\le U^{*}\le 20$. Two-dimensional computations are performed using an immersed boundary method with the cylinder initially at rest and are left to respond to the fluid forces from a height close to the wall. The cylinder is elastically mounted and has two degrees of freedom. A penalty type of collision model is employed where the repulsive force between the cylinder and wall springs into action beyond a critical separation and increases inversely with the gap. The cylinder response is synchronized with the near wake, and its transverse vibration frequency is twice the natural frequency. In the synchronization regime, three response branches are observed in the structural response curve: upper branch (UB), lower branch initial [LB(I)], and lower branch terminal [LB(T)]. Steady flow at low $U^{*}$ proceeds to the highly responsive UB at a threshold reduced velocity. The response curves remain unaltered with changes in gap ratios, whereas the critical threshold $U^{*}$ for the UB response branch moves with $m^{*}$. Transverse displacement of the cylinder is maximum in UB, followed by a dip in a narrow band of $U^{*}$ in LB(I), where the trajectories produce a perfect limit cycle. In the LB(T) branch though the transverse response stabilizes, and trajectories show quasiperiodic nature intermittently. Wake oscillations are found to peak in the UB branch with both drag and lift rms yielding high values, which subsequently settle down in the LB(T) branch at higher $U^{*}$. The wall-jet type gap flow between the cylinder and the wall deflects with the ascending and descending motion of the cylinder. We have devised a method for tracking vortex trajectories, which reveals vortex elongation, vortex merging, wake-wall interactions, and late-stage vortex merging at different response branches. We have identified a unique aspect of cylinder motion over the response branches: “impact” and “gracing.” The lift and transverse motion of the cylinder show discontinuity and rapid changes within a short time for the impact cases with a large repulsive force that has an impulsive nature. In contrast, a trivial repulsive force marks continuous lift and vertical motion of the cylinder in the gracing mode. The nature of the collision is inelastic for the impact cases for both mass and gap ratios. We have proposed a flow model for the downstream evolution of the streamwise velocity, which reveals the spatial transition. The model identifies three flow regimes: wall jet, separated shear flow, and far wake evolution. The upper branch does not favor the existence of a separated region, while the wall-jet flow becomes distinct in the LB(I). The streamwise evolution in the far wake shows a thicker reattached shear layer. The point of wall separation lies mostly upstream of the cylinder while the reattachment length becomes insensitive to $U^{*}$ for a lighter cylinder owing to a vigorous transverse vibration.

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• Flow-structure interactions
• Laminar flows
• Vortex dynamics