Titles and abstracts

TITLE: Reconnection of infinitely thin vortices and its relation to the finite thickness case

ABSTRACT: 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 vortices, e.g. condensation trails of an aircraft. During this process, the initially straight vortices undergo sinusoidal deformation called Crow waves and eventually intersect, giving rise to a cascade of coherent structures. Due to the finite thickness of the vortices, the definition of the reconnection time, the reconnection point, and extraction of the centerlines of the vortices after the reconnection are quite challenging tasks. However, the emerging structures, such as the horseshoe and helical waves, are very reminiscent of those observed in the evolution of infinitely thin polygonal vortex subject to the localized induction approximation (LIA). This raises the question: do vortices form a corner singularity during the reconnection? In this talk, we consider a LIA-based model of reconnection of infinitely thin vortices with an interaction term that allows the formation of a corner from initially smooth solution. We demonstrate that the eye-shaped vortex obtained after the reconnection can be recovered with another angles after a time $\pi / 2$ that is independent of the initial angle. Given that for finite thickness vortices it is difficult to extract the vortex centerline, we consider the fluid impulse, an integral quantity that can be defined for both the LIA and the solution of the Navier-Stokes equations. It turns out that this quantity can be very useful for determining the reconnection time and the reconnection points even for the case of vortices with finite thickness.