Title

Fully Nonlinear Local Induction Equation Describing The Motion Of A Vortex Filament Inâ Superfluid 4He

Keywords

Computational methods; Quantum fluids; Vortex dynamics

Abstract

We obtain the fully nonlinear local induction equation describing the motion of a vortex filament in superfluid 4He. 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 Schrödinger 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 4He. 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. © Copyright 2012 Cambridge University Press.

Publication Date

9-25-2012

Publication Title

Journal of Fluid Mechanics

Volume

707

Number of Pages

585-594

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1017/jfm.2012.308

Socpus ID

84866065751 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84866065751

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