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
ISSN
1539-3755
Recommended Citation
Van Gorder, Robert A., "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" (2013). Faculty Bibliography 2010s. 4792.
https://stars.library.ucf.edu/facultybib2010/4792
Comments
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