Vortex-induced vibration of a sphere close to or piercing a free surface

Vortex-induced vibration (VIV) of an elastically mounted sphere placed in proximity to or piercing a free-surface (FS) was investigated numerically. The effect of the free-surface was examined over the reduced velocity range 3.5 ≤ U^∗ ≤ 14, by systematically varying the submergence depth (h) between 1 and -5/8 sphere diameters (D). The fully-coupled fluid-structure system was solved assuming the flow is incompressible and treating the free-surface boundary as a non-deformable free-slip surface. In-line with previous experimental findings, the maximum sphere response amplitude was found to be sensitive to the submergence depth, and indeed the influence of submergence depth variation was stronger for the piercing-sphere cases, with the maximum response for h^∗ = -3/8. The varying near-wake vortex dynamics was examined in detail to understand the effect of h^∗ on the VIV response of the sphere. For piercing-sphere cases, two previously unseen vortical recirculation bubbles were formed behind the sphere near times of maximum displacement, enhancing the VIV response. These were strongest at h^∗ = -3/8, and much weaker for small submergence depths, explaining the observed response amplitude variation.