The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices
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.(Published Online April 20 2006)
(Received November 28 1983)
(Revised May 17 1984)
p1 Present address: Department of Mathematics, University of Arizona, Tucson.
p2 Present address: Chevron Oil Field Research, La Habra, California.