Fully nonlinear local induction equation describing the motion of a vortex filament in superfluid He-4

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Fluid Mech.

    Keywords

    Computational methods; Vortex dynamics; Quantum fluids; ROTATING HELIUM-II; KNOTS; APPROXIMATION; DYNAMICS; Mechanics; Physics, Fluids & Plasmas

    Abstract

    We obtain the fully nonlinear local induction equation describing the motion of a vortex filament in superfluid He-4. As the relevant friction parameters are small, we linearize terms involving such parameters, while keeping the remaining nonlinearities, which accurately describe the curvature of the vortex filament, intact. The resulting equation is a type of nonlinear Schrodinger equation, and, under an appropriate change of variables, this equation is shown to have a first integral. This is in direct analogy with the simpler equation studied previously in the literature; indeed, in the limit where the superfluid parameters are taken to zero, we recover the results of Van Gorder. While this first integral is mathematically interesting, it is not particularly useful for computing solutions to the nonlinear partial differential equation which governs the vortex filament. As such, we introduce a new change of dependent variable, which results in a nonlinear four-dimensional system that can be numerically integrated. Integrating this system, we recover solutions to the fully nonlinear local induction equation describing the motion of a vortex filament in superfluid He-4. We find that the qualitative features of the solutions depend not only on the superfluid friction parameters, but also strongly on the initial conditions taken, the curvature and the normal fluid velocity.

    Journal Title

    Journal of Fluid Mechanics

    Volume

    707

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    585

    Last Page

    594

    WOS Identifier

    WOS:000308584600029

    ISSN

    0022-1120

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