# Giorgio Krstulovic - Laboratoire J.L. Lagrange - Keywords: fluid dynamics, turbulence

Vortices naturally arise in fluids when they are stirred by some physical mechanism. Most common examples are tornadoes or the highly rotating zones in the wake of a plane. Different highly rotating zones of a fluid, usually concentrated on tubes or sheets, interact and can event reconnect. Such events are called vortex reconnections.

Vortex reconnections in fluids have been object of study for long time in the context of plasma physics and both classical and superfluid dynamics. Such reconnections are events characterized by a rearrangement in the topology of the vorticity field (the curl of the velocity). Such topological modifications are believed to play a fundamental role in several physical phenomena like eruptive solar events, energy transfer and fine-scale mixing and turbulent states in superfluids. Despite their physical relevance, reconnections represent also a stand-alone mathematical problem, related for instance, to the presence of singularities in the Euler equation.

In classical fluids described by the Navier-Stokes equation, reconnecting vortex tubes stretch and deform, leading to complicated dynamics and the formation of complex geometrical structures. In order to understand fundamental aspects of vortex reconnections it is often desirable to work with a vortex configuration where the vorticity results confined along lines with a core of zero size. Such idealization is called a vortex filament. This limit naturally arises in superfluids, such as superfluid liquid Helium (He II) and Bose--Einstein condensates. Superfluids are in fact examples of ideal flows of quantum mechanical nature characterized by the lack of viscous dissipation and by a Dirac's vorticity distribution supported on the vortex filaments. For such fluids, the velocity circulation (contour integral of the velocity) is quantized. Superfluids are thus a perfect setting to study some theoretical aspects of vortex reconnections.

In this talk Il will present recent results on superfluid vortex reconnections, based on numerical simulations and analytical calculations within the framework of the Gross-Pitaevskii model. The aim is to highlight what are the universal aspects of vortex reconnections.