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Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers

Published online by Cambridge University Press:  04 July 2007

L. PARRAS  and
R. FERNANDEZ-FERIA
L. PARRAS
Affiliation:
Universidad de Málaga, E.T.S. Ingenieros Industriales, Pza. El Ejido, s/n 29013 Málaga, Spain
R. FERNANDEZ-FERIA
Affiliation:
Universidad de Málaga, E.T.S. Ingenieros Industriales, Pza. El Ejido, s/n 29013 Málaga, Spain
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Abstract

Batchelor's vortex has been commonly used in the past as a model for aircraft trailing vortices. Using a temporal stability analysis, new viscous unstable modes have been found for the high swirl numbers of interest in actual large-aircraft vortices. We look here for these unstable viscous modes occurring at large swirl numbers (q > 1.5), and large Reynolds numbers (Re >103), using a spatial stability analysis, thus characterizing the frequencies at which these modes become convectively unstable for different values of q, Re, and for different intensities of the uniform axial flow. We consider both jet-like and wake-like Batchelor's vortices, and are able to analyse the stability for Re as high as 108. We also characterize the frequencies and the swirl numbers for the onset of absolute instabilities of these unstable viscous modes for large q.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 27 - 43
Copyright
Copyright © Cambridge University Press 2007

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