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Inviscid instability of the Batchelor vortex: Absolute-convective transition and spatial branches

Phys. Fluids 11, 1805 (1999); doi:10.1063/1.870045

Issue Date: July 1999

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Cornel Olendraru and Antoine Sellier
LadHyX, CNRS–UMR 7646, École Polytechnique, F-91128 Palaiseau Cedex, France

Maurice Rossi
Laboratoire de Modélisation en Mécanique (LMM), Université Paris VI, Tour 66, 4, place Jussieu, F-75252 Paris cedex 05, France

Patrick Huerre
LadHyX, CNRS–UMR 7646, École Polytechnique, F-91128 Palaiseau Cedex, France
The main objective of the study is to examine the spatio-temporal instability properties of the Batchelor q-vortex, as a function of swirl ratio q and external axial flow parameter a. The inviscid dispersion relation between complex axial wave number and frequency is determined by numerical integration of the Howard–Gupta ordinary differential equation. The absolute-convective nature of the instability is then ascertained by application of the Briggs–Bers zero-group-velocity criterion. A moderate amount of swirl is found to promote the onset of absolute instability. In the case of wakes, transition from convective to absolute instability always takes place via the helical mode of azimuthal wave number m = –1. For sufficiently large swirl, co-flowing wakes become absolutely unstable. In the case of jets, transition from absolute to convective instability occurs through various helical modes, the transitional azimuthal wave number m being negative but sensitive to increasing swirl. For sufficiently large swirl, weakly co-flowing jets become absolutely unstable. These results are in good qualitative and quantitative agreement with those obtained by Delbende et al. through a direct numerical simulation of the linear response. Finally, the spatial (complex axial wave number, real frequency) instability characteristics are illustrated for the case of zero-external flow swirling jets. ©1999 American Institute of Physics.
History: Received 29 May 1998; accepted 5 March 1999
Permalink: http://link.aip.org/link/?PHFLE6/11/1805/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.32.Cc
    Fluid dynamics Rotational flow and vorticity Vortex dynamics
  • 47.20.Cq
    Fluid dynamics Hydrodynamic stability Inviscid instability
  • 47.27.Te
    Fluid dynamics Turbulent flows, convection, and heat transfer Convection and heat transfer
  • 47.27.Vf
    Fluid dynamics Turbulent flows, convection, and heat transfer Wakes
  • 47.27.Wg
    Fluid dynamics Turbulent flows, convection, and heat transfer Jets
  • YEAR: 1999

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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REFERENCES (45)
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