  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.
