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

    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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