Reconnections of interacting hairpin vortices in axisymmetric free shear flows

Direct numerical simulations (DNS) are used to study the evolution of hairpin vortices to understand the late-stage turbulent breakdown of vortex rings. Several hairpin initial configurations with Reynolds number italic Re equals 1500 Re = 1500 $\textit{Re} = 1500$ were considered, both isolated and multiple. The isolated hairpins evolve in a quiescent flow, demonstrating reconnection events in stages (bridging, cut and reconnect, rapid separation of two parts, residual threads), similar to prior observations in antiparallel vortices. Next, multiple configurations of six hairpin vortices in a circular array are simulated, with the background flow extracted from the DNS of the near wake of a vortex ring undergoing azimuthal instability. Here, the alignment of vorticity at the tips with that of the azimuthal component of background flow vorticity is found to be an important parameter. When the vorticity components are opposite, hairpin tips deflect inward so that neighbouring hairpins also participate in reconnection events, yielding a complex set of reconnections, further amplified for staggered hairpins. Otherwise, hairpin tips deflect outwards and evolve much as an isolated hairpin. While higher italic Re Re $\textit{Re}$ makes the onset and reconnections faster, the extent of vortex stretching in the specific background flow relative to the viscous dissipation decides the temporal evolution of total enstrophy. It rises sharply just before reconnection events, falling rapidly afterwards, while for the DNS-extracted ring wake flow, the maximum enstrophy is higher compared with the simpler shear flows. Reconnection events distribute the energy over a broader spectrum, especially to higher wavenumbers.