Three-dimensional distortions of a vortex filament: Exact solutions of the localized induction equation

Yasuhide Fukumoto, Takeshi Miyazaki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The three-dimensional motion of a thin vortex filament in an inviscid incompressible fluid is investigated theoretically, on the basis of the localized induction equation(LIE). It is shown that the N-soliton solution, obtained through Hirota's bilinear method, does not exhibit clear phase-advance during head-on collisions as observed in the experiment by Maxworthy et al. In order to resolve this discrepancy an effect of axial flow within the vortex core is incorporated into the LIE and a new integrable equation is derived. The bilinear procedure as well as the soliton surface approach gives the N-soliton solution which is identical to that of the LIE except for the dispersion relation. Besides, this equation predicts that a certain class of helicoidal vortices with axial flow is neutrally stable against any small perturbations.

Original languageEnglish
Pages (from-to)157-162
Number of pages6
JournalFluid Dynamics Research
Volume3
Issue number1-4
DOIs
Publication statusPublished - Sep 1 1988
Externally publishedYes

Fingerprint

vortex filaments
Solitons
induction
Vortex flow
Axial flow
axial flow
solitary waves
three dimensional motion
vortices
incompressible fluids
Fluids
perturbation
Experiments
collisions

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

Cite this

Three-dimensional distortions of a vortex filament : Exact solutions of the localized induction equation. / Fukumoto, Yasuhide; Miyazaki, Takeshi.

In: Fluid Dynamics Research, Vol. 3, No. 1-4, 01.09.1988, p. 157-162.

Research output: Contribution to journalArticle

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