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Two-dimensional linear instability of a Lamb-Oseen counter-rotating vortex dipole

Jugier, Rémi and Joly, Laurent and Fontane, Jérôme and Brancher, Pierre Two-dimensional linear instability of a Lamb-Oseen counter-rotating vortex dipole. (2014) In: 67th Annual Meeting of the American Physical Society's Division of Fluid Dynamics (DFD), 23 November 2014 - 25 November 2014 (San Francisco, United States). (Unpublished)

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Abstract

The present study investigates the stability of a family of quasi-steady two-dimensional vortex dipoles resulting from the adaptation to the mutual deformation and viscous diffusion of counter-rotating Lamb-Oseen vortices of equal size and circulation. For sufficiently large Reynolds numbers, the internal structure is set by the dipole aspect ratio a/b (radius versus separation distance), giving rise to a family of smooth quasi-steady solutions. These base flow solutions consist of self-propagating dipoles with a vorticity trail leaking from the dipole during the self-adaptation process and from diffusion across the dipole Kelvin oval. The present work is a generalization of the recent study by Brion et al. (2014), who found that a specific kind of vortex dipole, the Lamb-Chaplygin dipole, was unstable with respect to two-dimensionnal perturbations. We show how the growth rate and spatial structure of the unstable modes vary with aspect ratio a/b and Reynolds number. The growth rates are lower than for the Lamb-Chaplygin dipole and decreases when the aspect ratio is lowered. It is advocated here that these new two-dimensional modes of small aspect-ratio smooth dipoles are good candidates for steady actuation in aircrafts conditions.

Item Type:Conference or Workshop Item (Speech)
Audience (conference):International conference without published proceedings
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
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Deposited By: Jérôme Fontane
Deposited On:06 Jan 2015 14:08

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