Linear stability of a vortex ring revisited

Yasuhide Fukumoto, Yuji Hattori

Research output: Chapter in Book/Report/Conference proceedingChapter


We revisit the stability of an elliptically strained vortex and a thin axisymmetric vortex ring, embedded in an inviscid incompressible fluid, to three-dimensional disturbances of infinitesimal amplitude. The results of Tsai & Widnall (1976) for an elliptically strained vortex are simplified by providing an explicit expression for the disturbance flow field. A direct relation is established with the elliptical instability. For Kelvin's vortex ring, the primary perturbation to the Rankine vortex is a dipole field. We show that the dipole field causes a parametric resonance instability between axisymmetric and bending waves at intersection points of the dispersion curves. It is found that the dipole effect predominates over the straining effect for a very thin core. The mechanism is attributable to stretching of the disturbance vortex lines in the toroidal direction.

Original languageEnglish
Title of host publicationTubes, Sheets and Singularities in Fluid Dynamics
PublisherKluwer Academic Publishers
Number of pages12
ISBN (Print)1402009801, 9781402009808
Publication statusPublished - 2004

Publication series

NameFluid Mechanics and its Applications
ISSN (Print)0926-5112

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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