A study of the reconnection of antiparallel vortices in the infinitely thin case and in the finite thickness case

The reconnection of vortices is an important example of the transition from laminar to turbulent flow. The simplest case is the reconnection of a pair of antiparallel line vortices. At first, they undergo long wave deformation (Crow waves), and then reconnect to form coherent structures. Although the behavior of the vortices before and after the reconnection can be clearly observed, what happens during the reconnection still needs to be explained. In fact, due to the finite thickness of the vortices, it is possible to distinguish different types of reconnection, such as reconnection of vorticity lines or reconnection of isosurfaces of vorticity magnitude. This makes unclear the definition of the reconnection time and reconnection point, which represents one major challenge. Note that the smallest scale of emerged coherent structures also depends on this thickness. In this paper, we consider an infinitely thin vortex approximation to study the vorticity reconnection process. We show that, in this case, the behavior after the reconnection is quasi-periodic, with the quasi-period being independent of the angle between the vortices. We observe a similarity between the behavior of the vortices in the reconnection region and the evolution of a corner of a polygonal vortex under the localized induction approximation, which may be considered as an indicator that the vortices form a corner at the reconnection. At the end, we compare the results with a solution of the Navier–Stokes equations for the reconnection of a pair of antiparallel vortices with finite thickness, where the pressure isosurfaces are used to visualize the reconnection process. We also use the fluid impulse to define the reconnection time, the reconnection point, and the quasi-period for this case.