### 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 language | English |
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Title of host publication | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium |

Pages | 77-87 |

Number of pages | 11 |

Volume | 6 |

Publication status | Published - 2008 |

Event | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation Duration: Aug 25 2006 → Aug 30 2006 |

### Publication series

Name | Solid Mechanics and its Applications |
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Volume | 6 |

ISSN (Print) | 18753507 |

### Other

Other | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence |
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Country | Russian Federation |

City | Moscow |

Period | 8/25/06 → 8/30/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*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).

**Analogy of a vortex-jet filament with the Kirchhoff elastic rod and its dynamical extension.** / Fukumoto, Yasuhide.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium.*vol. 6, Solid Mechanics and its Applications, vol. 6, pp. 77-87, IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Moscow, Russian Federation, 8/25/06.

}

TY - GEN

T1 - Analogy of a vortex-jet filament with the Kirchhoff elastic rod and its dynamical extension

AU - Fukumoto, Yasuhide

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84861153022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861153022&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781402067433

VL - 6

T3 - Solid Mechanics and its Applications

SP - 77

EP - 87

BT - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium

ER -