Linear stability of a vortex ring revisited

  • Yasuhide Fukumoto
  • Yuji Hattori
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)


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.


Linear Stability Vortex Ring Vortex Tube Dipole Field Disturbance Velocity 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Yasuhide Fukumoto
    • 1
  • Yuji Hattori
    • 2
  1. 1.Graduate School of MathematicsKyushu University 33FukuokaJapan
  2. 2.Faculty of EngineeringKyushu Institute of TechnologyKitakyushuJapan

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