Vortex ring–cylinder interactions: regimes, reconnection, and the role of topology

We investigate the interaction between vortex rings and cylindrical obstacles using direct numerical simulations across a wide range of geometric and dynamical parameters. The flow is characterised in terms of the diameter ratio between ring and object upper T Subscript upper D Baseline equals d divided by upper D T D = d / D $T_D = d/D$ , the Reynolds number based on circulation italic Re Subscript upper Gamma Re Γ $\\textit{Re}_\\varGamma$ , and the slenderness ratio upper Lamda Λ $\\varLambda$ . By systematically varying upper T Subscript upper D T D $T_D$ and italic Re Subscript upper Gamma Re Γ $\\textit{Re}_\\varGamma$ , we identify three distinct interaction regimes: the wire, cutting and wall regimes. In the wire regime ( upper T Subscript upper D Baseline less than or equivalent to 0.05 T D ≲ 0.05 $T_D \\lesssim 0.05$ ), the primary vortex ring survives the interaction with limited deformation, and carries a weak lobe of secondary vorticity generated by the object’s boundary layer. As upper T Subscript upper D T D $T_D$ increases, the interaction transitions to the cutting regime, where the ring is split into two secondary structures formed through the reconnection between boundary-layer and ring vorticity. For sufficiently large obstacles ( upper T Subscript upper D Baseline greater than or equivalent to 0.8