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Three-dimensional stability of vortex arrays

Published online by Cambridge University Press:  20 April 2006

A. C. Robinson  and
P. G. Saffman
A. C. Robinson
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena. California 91125
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena. California 91125
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Abstract

The stability to three-dimensional disturbances of three classical steady vortex configurations in an incompressible inviscid fluid is studied in the limit of small vortex cross-sectional area and long axial disturbance wavelength. The configurations examined are the single infinite vortex row, the Karman vortex street of staggered vortices and the symmetric vortex street. It is shown that the single row is most unstable to a two-dimensional disturbance, while the Karman vortex street is most unstable to a three-dimensional disturbance over a significant range of street spacing ratios. The symmetric vortex street is found to be most unstable to three-dimensional or two-dimensional symmetric disturbances depending on the spacing ratio of the street. Short remarks are made concerning the relevance of the calculations to the observed instabilities in free shear layer, wake and boundary-layer type flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 411 - 427
Copyright
© 1982 Cambridge University Press

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