https://doi.org/10.1140/epjb/e2002-00279-5
Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy
Graduate School of Mathematics and Space Environment Research Center, Kyushu University 33, Fukuoka 812-8581, Japan
Corresponding author: a yasuhide@math.kyushu-u.ac.jp
Received:
2
October
2001
Revised:
10
May
2002
Published online:
2
October
2002
Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations.
Using the method of matched asymptotic expansions in a small parameter ϵ, the ratio of core radius to curvature radius,
the velocity of a vortex filament is derived to 
,
whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account.
It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy.
PACS: 47.32.Cc – Vortex dynamics / 02.30.Ik – Integrable systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
