Synchronization between the vibrations of two cylinders in a staggered arrangement in steady flow

This study presents a two-degree-of-freedom (2-DOF) numerical investigation into vortex-induced vibrations (VIV) of staggered circular cylinders. Simulations were conducted with a mass ratio of 2.54 at a fixed Reynolds number of 150 across a range of streamwise (L_x = 3–5) and transverse (L_y = 0–2) spacings and reduced velocities (V_r = 2–16). The results show that the upstream cylinder (C1) displayed classical VIV behaviour with consistent lock-in near V_r = 4-6, while the downstream cylinder (C2) displayed more complex, configuration-dependent responses, including dual-frequency vibrations and, in some cases, irregular trajectories. Three distinct vibrations modes, synchronized, synchronization with beating, and desynchronized, were identified based on the frequency and phase relationship between the two cylinders. Desynchronized modes appeared in specific configurations, characterized by time-varying phase differences between −180° and 180°. Vorticity and trajectory analyses revealed that increasing spacing reduced wake interference on C2. The classification of flow regimes, vortex pairing and enveloping (VPE), induced separation (IS), and vortex impingement (VI), showed that changes in flow pattern are directly related to the synchronized (S), synchronization-with-beating (SB), and desynchronized (DS) vibration modes between the two cylinders. These findings address critical gaps in understanding desynchronized VIV in staggered systems and provide new insights into how spacing and reduced velocity govern vibration dynamics.