TY - JOUR
T1 - Analogy between a vortex-jet filament and the Kirchhoff elastic rod
AU - Fukumoto, Yasuhide
N1 - Funding Information:
I am grateful to S. Kawakubo and K. Nishinari for illuminating discussions. This work was supported in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2007/7
Y1 - 2007/7
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. It is shown that permanent form of a steadily translating vortex-jet filament is identical with equilibrium form of an inextensible elastic rod of circular cross-section. A variational principle is presented for the statics of an elastic rod with respect to the director field, which manifests the origin of this analogy.
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. It is shown that permanent form of a steadily translating vortex-jet filament is identical with equilibrium form of an inextensible elastic rod of circular cross-section. A variational principle is presented for the statics of an elastic rod with respect to the director field, which manifests the origin of this analogy.
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U2 - 10.1016/j.fluiddyn.2006.12.004
DO - 10.1016/j.fluiddyn.2006.12.004
M3 - Article
AN - SCOPUS:34250674162
VL - 39
SP - 511
EP - 520
JO - Fluid Dynamics Research
JF - Fluid Dynamics Research
SN - 0169-5983
IS - 7
ER -