Analogy of A Vortex-Jet Filament With The Kirchhoff Elastic Rod and Its Dynamical Extension
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.
KeywordsVortex filament axial flow localized induction hierarchy Kirchhoff elastic rod variational principle
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