# Topological Constraints in the Reconnection of Vortex Braids

## TL;DR

This paper investigates how the topology of vortex braids influences their relaxation and reconnection dynamics in high Reynolds number fluids, revealing a topological simplification and energy bounds during the process.

## Contribution

It demonstrates the role of vortex braid topology in fluid relaxation, deriving analytical bounds and showing topological simplification during reconnection at high Reynolds numbers.

## Key findings

- Topology simplifies into large-scale opposite swirl regions.
- Reconnection cascade facilitates topological change.
- Kinetic energy has a lower bound related to helicity.

## Abstract

We study the relaxation of a topologically non-trivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field -- characterized by braided vorticity field lines -- determines the dynamics, particularly the asymptotic behaviour under vortex reconnection in an evolution at high Reynolds numbers 25,000. Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process the existence of regions of positive and negative kinetic helicity imposes a lower bound for the kinetic energy. For the enstrophy we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments.