Vortex reconnection in the three dimensional Navier-Stokes equations

TL;DR

This paper demonstrates that vortex structures in 3D Navier-Stokes solutions can undergo topology changes without losing regularity, aligning with simulations and experiments, and introduces scenarios of vortex destruction.

Contribution

It constructs smooth solutions showing vortex reconnection with topological changes, a novel demonstration of reconnection in regular solutions of Navier-Stokes.

Findings

Vortex reconnection occurs without loss of regularity.

Constructed solutions exhibit complex vortex topology changes.

Reconnection scenarios match experimental observations.

Abstract

We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier-Stokes equations where vortex lines and vortex tubes of arbitrarily complicated topologies are created and destroyed in arbitrarily small times. This instance of vortex reconnection is structurally stable and in perfect agreement with the existing computer simulations and experiments. We also provide a (non-structurally stable) scenario where the destruction of vortex structures is instantaneous.