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Inviscid instability of an unbounded heterogeneous shear layer

Published online by Cambridge University Press:  29 March 2006

S. A. Maslowe  and
R. E. Kelly
S. A. Maslowe
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles, California 90024 Present address: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
R. E. Kelly
Affiliation:
School of Engineering and Applied Science, University of California, Los Angeles, California 90024
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Abstract

Stability curves are computed for both spatially and temporally growing disturbances in a stratified mixing layer between two uniform streams. The low Froude number limit, in which the effects of buoyancy predominate, and the high Froude number limit, in which the effects of density variation are manifested by the inertial terms of the vorticity equation, are considered as limiting cases. For the buoyant case, although the spatial growth rates can be predicted reasonably well by suitable use of the results for temporal growth, spatially growing disturbances appear to have high group velocities near the lower cutoff wave-number. For the inertial case, it is demonstrated that density variations can be destabilizing. More precisely, when the stream with the higher velocity has the lower density, both the wave-number range of unstable disturbances and the maximum spatial growth rate are increased relative to the case of homogeneous flow. Finally, it is shown how the growth rate of the most unstable wave in the inertial case diminishes as buoyancy becomes important.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 2 , 28 July 1971 , pp. 405 - 415
Copyright
© 1971 Cambridge University Press

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