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Published October 1984 | Published
Journal Article Open

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


The stability of two-dimensional infinitesimal disturbances of the inviscid Karman 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.

Additional Information

© 1984 Cambridge University Press. Received 28 November 1983; in revised form 17 May 1984. This work was started while P. G. S. was visiting the Mathematics Research Center, University of Wisconsin, Madison, and continued during a visit to the Mathematics Department, Massachusetts Institute of Technology. He wishes to thank both Institutes for support. The work was also supported by the Office of Naval Research, the Department of Energy (Office of Basic Energy Sciences) and NASA Lewis (NAG 3-179). Ms E. E. Saffman provided extensive help with many of the computations.

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August 19, 2023
October 17, 2023