Helicity Conservation, and Twisted Seifert Surfaces for Superfluid Vortices
arXiv:1706.03257 · doi:10.1098/rspa.2016.0853
Abstract
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterise the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times. It follows that the Gauss-linking number is a more appropriate definition of helicity for superfluids. Despite this, we explain how a quasiclassical limit can arise in a superfluid in which the continuum definition for helicity can be used. This provides a clear connection between a microscopic and a macroscopic description of a superfluid as provided by the Hall-Vinen-Bekarevich-Khalatnikov equations. This leads to consistency with the definition of helicity used for classical vortices.
References in corpus (18)
- Tying knots in light fields
- Knots in a Spinor Bose-Einstein Condensate
- How superfluid vortex knots untie
- Helicity conservation by flow across scales in reconnecting vortex links and knots
- Vortex knots in a Bose-Einstein condensate
- Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex
- Reconnection of superfluid vortex bundles
- Local phase structure of wave dislocation lines: twist and twirl
- Breathers on Quantized Superfluid Vortices
- Dynamics of quantum turbulence of different spectra
- Velocity, energy and helicity of vortex knots and unknots
- Vortex knots in tangled quantum eigenfunctions
- Helicity, Topology and Kelvin Waves in reconnecting quantum knots
- Helicity conservation under quantum reconnection of vortex rings
- Untangling knots via reaction-diffusion dynamics of vortex strings
- Excitation of knotted vortex lines in matter waves
- On the Burgers vector of a wave dislocation
- The Life of a Vortex Knot
Cited by in corpus (6)
- Crossover from interaction to driven regimes in quantum vortex reconnections
- Topological transition from superuid vortex rings to isolated knots and links
- A matching theory to characterize sound emission during vortex reconnection in quantum fluids
- Helicity in Superfluids: existence and the classical limit
- Finite temperature effects in helical quantum turbulence
- Mesoscale helicity distinguishes Vinen from Kolmogorov turbulence in helium II