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

TL;DR

This work addresses how vortex rings interact with cylindrical obstacles across a wide geometric and dynamical parameter space. Using direct numerical simulations, the authors map three principal interaction regimes—wire, cutting, and curved-wall—and show that regime transitions are primarily governed by the diameter ratio $T_D$, with Reynolds number $Re_\Gamma$ enriching the dynamics through enhanced stretching and reconnection. A central contribution is the demonstration that obstacle topology critically controls reconnection pathways and ring recovery, linking vortex-ring and vortex-tube collision behaviors and highlighting the role of boundary-layer vorticity. The results provide a unified framework for vortex–body interactions with potential applications to blade–vortex interactions, wakes around slender bodies, and turbulent flow interpretations in complex geometries.

Abstract

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 characterized in terms of the diameter ratio between ring and object $T_D = d/D$, the Reynolds number based on circulation $Re_Γ$, and the slenderness ratio $Λ$. By systematically varying $T_D$ and $Re_Γ$, we identify three distinct interaction regimes: the wire, cutting, and wall regimes. In the wire regime ($T_D \lesssim 0.05$), 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 $T_D$ 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 ($T_D \gtrsim 0.8$), the wall regime emerges, in which boundary-layer vorticity dominates and the primary ring is deflected and stretched along the obstacle surface. The transition between regimes depends primarily on $T_D$, while increasing $Re_Γ$ enhances vortical dynamics producing additional small-scale and tertiary structures. Finally, by modifying the topology of the obstacle, we demonstrate that reconnection and recovery of the primary ring depend critically on the topology of the secondary vorticity. These results provide a unified framework for interpreting vortex-body interactions, bridging the gap between vortex ring, tube, and wall collision dynamics.

Figures (20)

• Figure 1: Left: Schematic of a vortex ring approaching the cylinder-like object. The figure represents a cut of the system by a plane containing the ring's axis of symmetry, shown as a dashed line, and the cylinder's axis. Right: variation of impact parameter $I_P$ with ring slenderness $\sigma$ as in equation \ref{['eq:ipsigma']}. The shaded green region indicates the strong vortex regime.
• Figure 2: Volumetric visualization of the instantaneous vorticity modulus of the impact of a vortex ring with $\Lambda=0.2$ and $Re_\Gamma=1000$ upon a cylinder of varying diameter: (left to right: $T_D=0.025$, $0.1$, $0.4$, $1$ and $2$). Time ranges from $t=25$ to $65$ in intervals of $10$.
• Figure 3: Volumetric visualization of the instantaneous vorticity modulus of the impact of a vortex ring with $\Lambda=0.2$ and $Re_\Gamma=2000$ upon a cylinder of varying diameter: (left to right: $T_D=0.025$, $0.1$, $0.4$, $1$ and $2$). Time ranges from $t=25$ to $65$ in intervals of $10$, with the last snapshot at $t=85$.
• Figure 4: Volumetric visualization of the instantaneous vorticity modulus of a vortex ring impacting a wire at $Re_\Gamma=1000$. Left to right: $T_D=0.05$, $\Lambda=0.1$ ($T_\sigma=1$); $T_D=0.05$, $\Lambda=0.35$ ($T_\sigma=0.28$); $T_D=0.4$, $\sigma=0.1$ ($T_\sigma=8$); and $T_D=0.4$, $\sigma=0.35$ ($T_\sigma=2.3$). For $\sigma=0.1$, time ranges from $t=20$ to $50$ in intervals of $10$, while for $\sigma=0.35$ time ranges from $t=25$ to $70$ in intervals of $15$.
• Figure 5: Volumetric visualization of the instantaneous vorticity modulus of a vortex ring impacting a wire at $Re_\Gamma=2000$. Cases and times are the same as Figure \ref{['fig:crs-rcyls-re1000']}.