Vortex motion in superfluid He-4: effects of normal fluid flow

    Authors

    B. K. Shivamoggi

    Comments

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    Abbreviated Journal Title

    Eur. Phys. J. B

    Keywords

    ROTATING HELIUM-II; LIQUID HELIUM; QUANTIZED VORTICES; FILAMENT; DYNAMICS; TURBULENCE; EQUATIONS; WAVES; Physics, Condensed Matter

    Abstract

    The motion of a vortex filament in superfluid He-4 is considered by using the Hall-VinenBekarevich-Khalatnikov (HVBK) [H. E. Hall, W. F. Vinen, Proc. Roy. Soc. Lond. A 238, 204 (1956); H. E. Hall, W. F. Vinen, Proc. Roy. Soc. Lond. A 238, 215 (1956); I. L. Bekarevich, I. M. Khalatnikov, Sov. Phys. J. Exp. Theor. Phys. 13, 643 (1961)] phenomenological model for the scattering process between the vortex and thermal excitations in liquid He-4. The HVBK equations are analytically formulated first in the intrinsic geometric parameter space to obtain insights into the physical implications of the friction terms, associated with the friction coefficients alpha and alpha ' (in the Hall-Vinen notation) as well as the previous neglect of the friction term associated with the friction coefficient alpha '. The normal fluid velocity components both along and transverse to the vortex filament are included. This analytical development also serves to highlight the difficulties arising in making further progress on this route. A reformulation of the HVBK equation in the extrinsic vortex filament coordinate space is then given which is known [B. K. Shivamoggi, Phys. Rev. B 84, 012506 (2011)] to provide a useful alternative analytical approach in this regard. A nonlinear Schrodinger equation for the propagation of nonlinear Kelvin waves on a vortex filament in a superfluid is given taking into account the generalized normal fluid flow. The friction term associated with alpha ', even in the presence of the normal fluid velocity components transverse to the vortex filament, is shown to produce merely an algebraic growth of the Kelvin waves hence providing further justification for the neglect of this term. On the other hand, the instability produced by the friction term associated with alpha via the normal fluid velocity component along the vortex filament is shown to manifest itself as a parametric amplification on considering the problem of a rotating planar vortex filament in a superfluid.

    Journal Title

    European Physical Journal B

    Volume

    86

    Issue/Number

    6

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    7

    WOS Identifier

    WOS:000321446200035

    ISSN

    1434-6028

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