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Linear stability of a vortex ring revisited

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

Abstract

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.

Keywords

Linear Stability Vortex Ring Vortex Tube Dipole Field Disturbance Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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