Title

Scaling laws and accurate small-amplitude stationary solution for the motion of a planar vortex filament in the Cartesian form of the local induction approximation

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Phys. Rev. E

Keywords

EQUATIONS; KNOTS; INVARIANTS; Physics, Fluids & Plasmas; Physics, Mathematical

Abstract

We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrodinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely. DOI: 10.1103/PhysRevE.87.043203

Journal Title

Physical Review E

Volume

87

Issue/Number

4

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

8

WOS Identifier

WOS:000317913700006

ISSN

1539-3755

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