The 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

doi:10.1103/physreve.57.5276

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arXiv · patt-sol/9712004

The 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

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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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I. S. Aranson, A. R. Bishop, L. Kramer. 1997-12-09. The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices. https://doi.org/10.1103/physreve.57.5276

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