Mechanisms of double-lock-in vortex-induced vibration of the 5:1 rectangular cylinder

This study experimentally investigates the mechanisms of the double-lock-in vortex-induced vibration (VIV) of the rectangular cylinder with a width-to-height ratio of B/D = 5, through synchronized measurements of vibration response, surface pressure, and particle image velocimetry, complemented by phase-averaged analysis and proper orthogonal decomposition (POD). The amplitude response reveals two well-separated lock-in regions: a small-amplitude branch (peak 0.012 D ) at reduced velocities U r ≈ 4.87–5.86 and a large-amplitude branch (peak 0.034 D ) at U r ≈ 9.08–12.73. The two branches produce fundamentally different pressure distributions and flow structures. The small-amplitude branch is characterized by multiple C p ' peaks, associated with paired leading-edge vortices (LEVs) that merge with trailing-edge vortex (TEV) and subsequently shed into the wake. The large-amplitude branch, in contrast, exhibits a single extended region of intense pressure fluctuations with a maximum C p ' ≈ 0.22, driven by a single LEV that merges with the TEV to form an impinging leading-edge vortex. Despite this contrast in vortex topology, phase-averaged hysteresis loops yield nearly identical relative aerodynamic work contributions for the two branches (~68–70% positive, ~30–32% negative). POD analysis reveals that the small-amplitude branch concentrates only 30.13% of the fluctuating energy in its dominant flow mode, whereas the large-amplitude branch concentrates 46.53%, augmented by additional harmonic flow modes (4.34%), yielding a combined VIV-driving energy fraction of 50.87%. The square of the energy ratio, (50.87% / 30.13%) 2 ≈ 2.85, closely matches the measured amplitude ratio (0.034 D / 0.012 D ≈ 2.83). This quantitative correspondence, observed under the two peak-response conditions examined, suggests that the VIV amplitude scales with the square of the energy fraction of the dominant flow mode, provided that the two branches operate with comparable relative aerodynamic work efficiency.