A model of vortex reconnection

Abstract

A model is proposed to describe the breaking and rejoining of vortex lines which occurs when vortex filaments of equal and opposite strengths touch. It is based on the idea that viscosity cancels the vorticity where the filaments first touch. The weakening of the centrifugal force in the vortex core then leads to a local increase in the pressure which accelerates the fluid in the cores in the axial direction and convects the vorticity away from the initial contact and produces an apparent rejoining. Hyperbolic equations to describe the process are formulated and numerical solutions are obtained. Estimates of the timescales are made and compared with the experimental data of Schatzle (1987). Reasonable agreement is found.