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Elliptic instability of a curved Batchelor vortex

Published online by Cambridge University Press:  09 September 2016

Francisco J. Blanco-Rodríguez  and
Stéphane Le Dizès
Francisco J. Blanco-Rodríguez
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, F-13013 Marseille, France
Stéphane Le Dizès*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, F-13013 Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

The occurrence of the elliptic instability in rings and helical vortices is analysed theoretically. The framework developed by Moore & Saffman (Proc. R. Soc. Lond. A, vol. 346, 1975, pp. 413–425), where the elliptic instability is interpreted as a resonance of two Kelvin modes with a strained induced correction, is used to obtain the general stability properties of a curved and strained Batchelor vortex. Explicit expressions for the characteristics of the three main unstable modes are obtained as a function of the axial flow parameter of the Batchelor vortex. We show that vortex curvature adds a contribution to the elliptic instability growth rate. The results are applied to a single vortex ring, an array of alternate vortex rings and a double helical vortex.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 224 - 247
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Copyright
© 2016 Cambridge University Press 

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