Analogy of a vortex-jet filament with the Kirchhoff elastic rod and its dynamical extension

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Abstract

Motion of a vortex filament with axial flow in the core, i.e. a vortex-jet filament, is governed, in the localized induction approximation, by the first two terms of the localized induction hierarchy. Permanent form of a steadily translating vortexjet filament is found to be identical with equilibrium form of a thin inextensible elastic rod of circular cross section, and, as a dynamical extension, traveling waves on an extensible rod is sought. We establish a variational principle for motion of an elastic rod with respect to material frames.

Original languageEnglish
Title of host publicationIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
Pages77-87
Number of pages11
Volume6
Publication statusPublished - 2008
EventIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation
Duration: Aug 25 2006Aug 30 2006

Publication series

NameSolid Mechanics and its Applications
Volume6
ISSN (Print)18753507

Other

OtherIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
CountryRussian Federation
CityMoscow
Period8/25/068/30/06

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All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Automotive Engineering
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Acoustics and Ultrasonics

Cite this

Fukumoto, Y. (2008). Analogy of a vortex-jet filament with the Kirchhoff elastic rod and its dynamical extension. In IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium (Vol. 6, pp. 77-87). (Solid Mechanics and its Applications; Vol. 6).