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Stochastic forcing of the Lamb–Oseen vortex

Published online by Cambridge University Press:  01 October 2008

J. FONTANE ,
P. BRANCHER  and
D. FABRE
J. FONTANE
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université Paul Sabatier, 2 Allée du Professeur Camille Soula, 31400 Toulouse, France
P. BRANCHER
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université Paul Sabatier, 2 Allée du Professeur Camille Soula, 31400 Toulouse, France
D. FABRE
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université Paul Sabatier, 2 Allée du Professeur Camille Soula, 31400 Toulouse, France
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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 into aircraft wakes, 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 characterized 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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 233 - 254
Copyright
Copyright © Cambridge University Press 2008

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