Short-wavelength stability analysis of thin vortex rings

Y. Hattori, Y. Fukumoto

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The linear stability of thin vortex rings are studied by short-wavelength stability analysis. The modified Hill-Schrsodinger equation for vortex rings, which incorporates curvature effect, is derived. It is used to evaluate growth rates analytically. The growth rates are also evaluated by numerical calculation and they agree well with analytical values for small ε which is the ratio of core radius to ring radius. Two types of vortex rings are considered: Kelvin's vortex ring and a Gaussian vortex ring. For Kelvin's vortex ring the maximum first-order growth rate is found to be 165/356ε. For the Gaussian vortex ring the first-order growth rate is large in the skirts of the vortex core. The first-order instability is significant for both vortex rings.

Original languageEnglish
Pages (from-to)3151-3163
Number of pages13
JournalPhysics of Fluids
Volume15
Issue number10
DOIs
Publication statusPublished - Oct 2003

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vortex rings
wavelengths
skirts
radii
curvature
vortices
rings

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics

Cite this

Short-wavelength stability analysis of thin vortex rings. / Hattori, Y.; Fukumoto, Y.

In: Physics of Fluids, Vol. 15, No. 10, 10.2003, p. 3151-3163.

Research output: Contribution to journalArticle

Hattori, Y. ; Fukumoto, Y. / Short-wavelength stability analysis of thin vortex rings. In: Physics of Fluids. 2003 ; Vol. 15, No. 10. pp. 3151-3163.
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