We perform numerical experiments of relaxing and reconnecting vortex braids. While these braids have no net kinetic helicity, they are topologically non-trivial. Similar experiments with magnetic braids in MHD have shown a non-trivial relaxation behavior that resulted in two distinct twisted flux tubes. Here we observe the same separation behavior. Furthermore, we show analytically and experimentally that the presence of unsigned kinetic helicity poses a lower bound for the enstrophy of the system, similar to the realizability condition in MHD. Lastly, even the kinetic energy appears limited from below by the unsigned helicity, although we do not have an analytical explanation for this.

1. Vortex Reconnection and
the Role of Topology
Simon Candelaresi, Gunnar Hornig,
Benjamin Podger, David I. Pontin

2. Magnetic Case
Conservation of magnetic helicity:
magnetic resistivity
Realizability condition:
Magnetic energy is bound from
below by magnetic helicity.
2

3. Magnetic Braid
(Wilmot-Smith 2010)
(Yeates 2011)
Separation into two twisted field
regions.
Conserved invariants like fixed
point index and field line helicity.
3

4. Navier-Stokes Case
4
No realizability condition for the hydro case.
How does the field line topology affect the dynamics?

5. Vortex Braid Experiments
5
Full viscous simulations with the PencilCode.
periodic
periodic
closed

6. Vortex Reconnection
6
Field lines untangle into two twisted vortex tubes.

7. Kinetic Energy Bound
7
Field topology
affects relaxation.
free kinetic energy:
unsigned kinetic helicity:

8. Vortex Braid Enstrophy
8
Hydrodynamical realizability condition.
enstrophy:
depends on the geometry of the domain.

9. Conclusions
●
Topology preserving relaxation of vortex fields.
●
Unbraiding into two twisted vortex flux tubes.
●
Unsigned helicity limits energy decay.
●
Realizability condition with enstrophy.
simon.candelaresi@gmail.com
Physics of Fluids 33, 056101 (2021); doi.org/10.1063/5.0047033

10. BlenDaViz
github.com/SimonCan/BlenDaViz