Reconnection of infinitely thin antiparallel vortices and coherent structures

Abstract

One of the characteristic features of turbulent flows is the emergence of many vortices which interact, deform, and intersect, generating a chaotic movement. The evolution of a pair of vortices, e.g. condensation trails of a plane, can be considered as a basic element of a turbulent flow. This simple example nevertheless demonstrates very rich behavior which still lacks a complete explanation. In particular, after the reconnection of the vortices some coherent structures with the shape of a horseshoe emerge. They have a high level of complexity generated by the interaction of waves running from the reconnection region. These structures also turn to be very reminiscent to the ones obtained from the localized induction approximation applied to a polygonal vortex. It can be considered as an evidence that a pair of vortices creates a corner singularity during the reconnection. In this work we focus on a study of the reconnection phenomena and the emerged structures. In order to do it we present a new model based on the approximation of an infinitely thin vortex, which allows us to focus on the chaotic movement of the vortex center line. The main advantage of the developed model consists in the ability to go beyond the reconnection time and to see the coherent structures. It is also possible to define the reconnection time by analyzing the fluid impulse.