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The two- and three-dimensional instabilities of a spatially periodic shear layer

Published online by Cambridge University Press:  20 April 2006

R. T. Pierrehumbert  and
S. E. Widnall
R. T. Pierrehumbert
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139 Present address: Department of Meteorology, Massachusetts Institute of Technology, Cambridge, MA 02139.
S. E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

The two- and three-dimensional stability properties of the family of coherent shear-layer vortices discovered by Stuart are investigated. The stability problem is formulated as a non-separable eigenvalue problem in two independent variables, and solved numerically using spectral methods. It is found that there are two main classes of instabilities. The first class is subharmonic, and corresponds to pairing or localized pairing of vortex tubes; the pairing instability is most unstable in the two-dimensional limit, in which the perturbation has no spanwise variations. The second class repeats in the streamwise direction with the same periodicity as the basic flow. This mode is most unstable for spanwise wavelengths approximately 2/3 of the space between vortex centres, and can lead to the generation of streamwise vorticity and coherent ridges of upwelling. Comparison is made between the calculated instabilities and the observed pairing, helical pairing, and streak transitions. The theoretical and experimental results are found to be in reasonable agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 59 - 82
Copyright
© 1972 Cambridge University Press

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