The role of three-dimensionality in wake synchronization characteristics of an oscillatory circular cylinder*

We examine how the three-dimensionality of the wake influences the synchronization characteristics of a circular cylinder at Reynolds number of 300. We determine the theoretical amplitude and frequency conditions that lead to synchronization from the phase-reduction analysis, which projects the full physics of periodic flows to just the phase plane. By comparing a forced two-dimensional wake to a natural three-dimensional wake, we identify the linear effect that wake three-dimensionality plays in reducing the synchronizability of the wake. Phase-reduction analysis, combined with synchronization boundaries obtained from direct numerical simulations, uncover the nonlinear influence of wake three-dimensionality. We found that the chaotic nature of three-dimensional wakes suppresses synchronization to small amplitude cylinder oscillations, while the transition from three- to two-dimensional flow at high-frequency oscillation brings additional capability for synchronization.