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Absolute and convective instabilities in free shear layers

Published online by Cambridge University Press:  20 April 2006

P. Huerre  and
P. A. Monkewitz
P. Huerre
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90089–0192
P. A. Monkewitz
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California at Los Angeles, Los Angeles, California 90024
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Abstract

The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio $R = \Delta U/2\overline{U}$, where ΔU is the velocity difference between the two streams and $\overline{U}$ their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 151 - 168
Copyright
© 1985 Cambridge University Press

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