Dynamics of vortex lines in the three-dimensional complex ginzburg-landau equation: instability, stretching, entanglement, and helices

I. S. Aranson, A. R. Bishop, L. Kramer

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.

Original languageEnglish (US)
Pages (from-to)5276-5286
Number of pages11
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume57
Issue number5
DOIs
StatePublished - Jan 1 1998

Fingerprint

Complex Ginzburg-Landau Equation
Landau-Ginzburg equations
Helix
Entanglement
helices
Vortex
vortices
Three-dimensional
Line
vortex filaments
Vortex Filament
Straight
Parameter Space
Saturation
Unstable
saturation
Configuration
configurations
Range of data

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

Cite this

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abstract = "The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.",
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AB - The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.

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