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Stochastic forcing of the Lamb–Oseen vortex

Fontane, Jérôme and Brancher, Pierre and Fabre, David Stochastic forcing of the Lamb–Oseen vortex. (2008) Journal of Fluid Mechanics, 613. 233-254. ISSN 1469-7645

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Official URL: http://dx.doi.org/10.1017/S002211200800308X

Abstract

The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected in aircraft wake, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterised by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex-turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vortex, a feature very similar to the phenomenon of vortex meandering (or wandering) observed experimentally, corresponding to an erratic displacement of the vortex core. At smaller wavelengths, we find that stochastic forcing can excite specific oscillating modes of the Lamb–Oseen vortex. More precisely, damped critical-layer modes can emerge via a resonance mechanism. For perturbations with higher azimuthal wavenumber m > 2, we find no structure that clearly dominates the response of the vortex.

Item Type:Article
Additional Information:Thanks to Cambridge University Press editor.The definitive version is available at http://journals.cambridge.org The original PDF of the article can be found at Journal of Fluid Mechanics website : http://dx.doi.org/10.1017/S002211200800308X
HAL Id:hal-00776519
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
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 > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited By: Jérôme Fontane
Deposited On:11 Jan 2013 13:19

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