On the cross-flow vibration response and vortex dynamics of a circular cylinder under combined current–oscillatory flows

This study examines the cross-flow vortex-induced vibration (VIV) of a circular cylinder in combined current–oscillatory inflows, revealing a distinct multi-frequency response characterised by beat-like modulation. Systematic water-channel experiments were conducted across a range of reduced velocities, inflow oscillation intensities and frequency ratios to investigate the synchronisation mechanisms among inflow velocity variations, cylinder motion and hydrodynamic loading. Results show that the presence of oscillatory inflow can lead to significant deviations of vibration amplitudes from quasi-steady predictions within the upper-branch regime. At a given reduced velocity, the cylinder motion is dominated by a primary frequency component similar to that observed in steady flow, but accompanied by two secondary components. The contributions of these supplementary frequencies increase with inflow oscillation intensity but diminish as the oscillation frequency rises. Analysis of time-varying hydrodynamic forces reveals that, in the upper-branch regime, the vortex-force phase angle deviates substantially from quasi-steady estimation based on instantaneous reduced velocity, which is associated with non-quasi-steady vortex-shedding patterns. Particle image velocimetry measurements reveal that when the minimum vortex-force phase angle lies between 0 $^\circ$ and 180 $^\circ$ over the inflow oscillation cycle, a mixed vortex-shedding mode emerges. This mode is characterised by a vortex sequence resembling the ‘2P’ (two-pair) shedding pattern but with negligible secondary vortices, occurring predominantly during intervals of low inflow velocity. A theoretical framework incorporating nonlinear damping and excitation coefficients assuming quasi-steady response well predicts VIV amplitudes and elucidates the influence of inflow oscillation intensity and frequency on the emergence of supplementary vibration frequencies.