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The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices

Published online by Cambridge University Press:  20 April 2006

D. I. Meiron ,
P. G. Saffman  and
J. C. Saffman
D. I. Meiron
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, Cal 91125 Present address: Department of Mathematics, University of Arizona, Tucson.
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, Cal 91125
J. C. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, Cal 91125 Present address: Chevron Oil Field Research, La Habra, California.
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Abstract

The stability of two-dimensional infinitesimal disturbances of the inviscid Kármán vortex street of finite-area vortices is reexamined. Numerical results are obtained for the growth rate and oscillation frequencies of disturbances of arbitrary subharmonic wavenumber and the stability boundaries are calculated. The stabilization of the pairing instability by finite area demonstrated by Saffman & Schatzman (1982) is confirmed, and also Kida's (1982) result that this is not the most unstable disturbance when the area is finite. But, contrary to Kida's quantitative predictions, it is now found that finite area does not stabilize the street to infinitesimal two-dimensional disturbances of arbitrary wavelength and that it is always unstable except for one isolated value of the aspect ratio which depends upon the size of the vortices. This result does agree, however, with those of a modified version of Kida's analysis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 187 - 212
Copyright
© 1984 Cambridge University Press

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