Helicity conservation and twisted Seifert surfaces for superfluid vortices

Salman, Hayder (2017) Helicity conservation and twisted Seifert surfaces for superfluid vortices. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 473 (2200).

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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 characterize 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 quasi-classical 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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 23 May 2017 05:05
Last Modified: 31 Oct 2019 15:11
URI: https://ueaeprints.uea.ac.uk/id/eprint/63588
DOI: 10.1098/rspa.2016.0853

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