Direct numerical simulation is carried out to study the response of an oscillating cylinder in uniform flow and in the wake of an upstream cylinder. It is found that the response of the cylinder wake is either a periodic (lock-in) or a quasi-periodic (non-lock-in) state. In the lock-in state, the vortex shedding frequency equals the forcing frequency. In the non-lock-in state, the shedding frequency shows a smooth variation with the driving frequency. For a cylinder oscillating in uniform flow, a lock-in diagram of different forcing amplitude is computed. However, no clear chaotic behaviour is detected near the lock-in boundary. For a cylinder oscillating in the wake of an upstream cylinder, the response state is strongly influenced by the distance between the two cylinders. By changing cylinder spacing, two different flow regimes are identified. In the ‘vortex formation regime’, found at large spacings, the vortex street develops behind both the upstream and downstream cylinders. The strength of the naturally produced oscillation upstream of the second cylinder becomes important compared to the forced oscillation and dominates the flow, leading to a very small or even indistinguishable zone of synchronization. However, in the ‘vortex suppression regime’, observed at small spacings, the oncoming flow to the downstream cylinder becomes so weak that it hardly affects its vortex wake, and therefore a large zone of synchronization is obtained. The numerical results are in good agreement with available experimental data.
