Short-wavelength stability analysis of thin vortex rings

Y. Hattori; Y. Fukumoto

doi:10.1063/1.1606446

Short-wavelength stability analysis of thin vortex rings

Y. Hattori, Y. Fukumoto

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

33 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 language	English
Pages (from-to)	3151-3163
Number of pages	13
Journal	Physics of Fluids
Volume	15
Issue number	10
DOIs	https://doi.org/10.1063/1.1606446
Publication status	Published - Oct 2003

All Science Journal Classification (ASJC) codes

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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10.1063/1.1606446

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AB - 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.

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Short-wavelength stability analysis of thin vortex rings

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