Elliptic instability of a curved Batchelor vortex. (9th September 2016)

• Record Type: Journal Article
• Authors: Blanco-Rodríguez, Francisco J.; Le Dizès, Stéphane
• Is Part Of: Journal of fluid mechanics. Volume 804(2016:Oct.)
• Page Start: 224
• Page End: 247
• Publication Date: 2016-09-09
• Subjects: vortex flows, -- vortex instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.533
• Languages: English
• ISSNs: 0022-1120

Abstract

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.