Vortex-induced vibration of a streamwise and transversely rotating sphere

We investigate the effect of streamwise and transverse rotation on the wake behind an elastically mounted sphere. Simulations are performed at a Reynolds number $Re=500$ over a range of reduced velocity 2≤ U≤ 12 , considering a low and high rotational speed (0.2 and 1), keeping the mass ratio m=2 . Streamwise rotation yields a structural response akin to the non-rotating case, while transverse rotation triggers induced vibration at lower U and sustains it across a wider range. Like the non-rotating case, the streamwise rotating sphere exhibits synchronous, high-amplitude vibration across the entire U^ range, whereas for low transverse rotation, it is confined to 5≤ U≤ 6 . Cross-stream displacement of the sphere remains unaffected by streamwise rotation with increasing U . In contrast, it monotonically increases due to transverse rotation, driven by the Magnus force, as supported by our theoretical and numerical estimations. While the spiral shedding mode dominates at Ω ₓ=0.2 , twisted hairpin and twisted spiral modes emerge as the rotation rate is increased. On the other hand, we observe the hairpin (HP) mode, as seen in the non-rotating case, for low transverse rotation. The HP mode gives rise to the ring vortical mode at the far wake, and with an increase in U^ , the wake shows small-scale stretched threads and reconnected bridgelets. Wake fluctuations increase with a streamwise rotation that saturates at higher U during synchronisation, while desynchronisation at dimensionless transverse rotation rate Ω z=1 induces intermittent low-amplitude vibration via the Magnus effect. Space–time reconstruction at the near wake shows an undisturbed helical vortex core at Ω ₓ=0.2 and U=5 , which bifurcates at Ω ₓ=1 owing to the centrifugal-induced distortion. At Ω ₓ=1 and U=5 , the phase difference between (y, Cy) and (z, Cz) exhibits in-phase synchrony with occasional phase slips. The wake vortex remains unaffected by the transverse rotation of the sphere; however, a streamwise rotating sphere couples the wake, leading to a rotational lock-in. The wake rotation shifts from anti-clockwise to clockwise sense earlier (in U^ ) at a lower rotation rate. The reduced velocity is seen to have a favourable effect on the transfer of the sphere’s rotational inertia onto the wake as the measured penetration depth increases with U . Insights from the present research will aid in understanding complex flow interactions in rotational systems, improving efficiency, stability and control in modern engineering applications.