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.

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U2 - 10.1007/978-1-4020-6744-0_7

DO - 10.1007/978-1-4020-6744-0_7

M3 - Conference contribution

AN - SCOPUS:84861153022

SN - 9781402067433

T3 - Solid Mechanics and its Applications

SP - 77

EP - 87

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

PB - Springer Verlag

T2 - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

Y2 - 25 August 2006 through 30 August 2006

ER -