Vortex Reconnection as the Dissipative Scattering of Dipoles

TL;DR

This paper presents a phenomenological model of vortex tube reconnection at high Reynolds numbers, describing vortex interactions as dipoles and fitting experimental data on vortex ring collisions.

Contribution

It introduces a novel dipole-based model for vortex reconnection, incorporating electrostatic analogies and statistical ensemble methods, to explain vortex interactions and match experimental observations.

Findings

Model accurately fits experimental data on symmetric vortex ring collisions.

Describes vortex line reshuffling via dipole directional transitions.

Extends to asymmetric reconnection of non-parallel vortex tubes.

Abstract

We propose a phenomenological model of vortex tube reconnection at high Reynolds numbers. The basic picture is that squeezed vortex lines, formed by stretching in the region of closest approach between filaments, interact like dipoles (monopole-antimonopole pairs) of a confining electrostatic theory. The probability of dipole creation is found from a canonical ensemble spanned by foldings of the vortex tubes, with temperature parameter estimated from the typical energy variation taking place in the reconnection process. Vortex line reshuffling by viscous diffusion is described in terms of directional transitions of the dipoles. The model is used to fit with reasonable accuracy experimental data established long ago on the symmetric collision of vortex rings. We also study along similar lines the asymmetric case, related to the reconnection of non-parallel vortex tubes.