Title

Dynamics of a planar vortex filament under the quantum local induction approximation

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Proc. R. Soc. A-Math. Phys. Eng. Sci.

Keywords

vortex dynamics; vortex filament; superfluid dynamics; integrable models; ROTATING HELIUM-II; SUPERFLUID HE-4; MOTION; INSTABILITY; Multidisciplinary Sciences

Abstract

The Hasimoto planar vortex filament is one of the rare exact solutions to the classical local induction approximation (LIA). This solution persists in the absence of friction or other disturbances, and it maintains its form over time. As such, the dynamics of such a filament have not been extended to more complicated physical situations. We consider the planar vortex filament under the quantum LIA, which accounts for mutual friction and the velocity of a normal fluid impinging on the filament. We show that, for most interesting situations, a filament which is planar in the absence of mutual friction at zero temperature will gradually deform owing to friction effects and the normal fluid flow corresponding to warmer temperatures. The influence of friction is to induce torsion, so the filaments bend as they rotate. Furthermore, the flow of a normal fluid along the vortex filament length will result in a growth in space of the initial planar perturbations of a line filament. For warmer temperatures, these effects increase in magnitude, since the growth in space scales with the mutual friction coefficient. A number of nice qualitative results are analytical in nature, and these results are verified numerically for physically interesting cases.

Journal Title

Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences

Volume

470

Issue/Number

2172

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

13

WOS Identifier

WOS:000344092400006

ISSN

1364-5021

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