Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

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Abstract

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter e, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(∈3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first, and third terms of the localized induction hierarchy.

Original languageEnglish
Pages (from-to)167-171
Number of pages5
JournalEuropean Physical Journal B
Volume29
Issue number2
DOIs
Publication statusPublished - Sep 2 2002

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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