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The stability of short waves on a straight vortex filament in a weak externally imposed strain field

Published online by Cambridge University Press:  29 March 2006

Chon-Yin Tsai  and
Sheila E. Widnall
Chon-Yin Tsai
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
Sheila E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
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Abstract

The stability of short-wave displacement perturbations on a vortex filament of constant vorticity in a weak externally imposed strain field is considered. The circular cross-section of the vortex filament in this straining flow field becomes elliptical. It is found that instability of short waves on this strained vortex can occur only for wavelengths and frequencies at the intersection points of the dispersion curves for an isolated vortex. Numerical results show that the vortex is stable at some of these points and unstable at others. The vortex is unstable at wavelengths for which ω = 0, thus giving some support to the instability mechanism for the vortex ring proposed recently by Widnall, Bliss & Tsai (1974). The growth rate is calculated by linear stability theory. The previous work of Crow (1970) and Moore & Saffman (1971) dealing with long-wave instabilities is discussed as is the very recent work of Moore & Saffman (1975).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 4 , 24 February 1976 , pp. 721 - 733
Copyright
© 1976 Cambridge University Press

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References

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