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On the three families of instability waves of high-speed jets

Published online by Cambridge University Press:  26 April 2006

Christopher K. W. Tam  and
Fang Q. Hu
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, USA
Fang Q. Hu
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-3027, USA
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Abstract

In this paper the normal-mode small-amplitude waves of high-speed jets are investigated analytically and computationally. Three families of instability waves, each having a distinct wave pattern and propagation characteristics, have been found. One of the families of waves is the familiar Kelvin-Helmholtz instability wave. The other two families of waves do not appear to have been clearly identified and systematically studied before. Waves of one of the new wave family propagate with supersonic phase velocities relative to the ambient gas. They are, therefore, referred to as supersonic instability waves. Waves of the other family have subsonic phase velocities. Accordingly they are called subsonic waves. The subsonic waves have the unusual property that they are unstable only for jets with finite thickness mixing layers. They are neutral waves when calculated by a vortex-sheet jet model.

Earlier Oertel (1979, 1980, 1982) using a novel optical technique observed in a series of experiments three sets of waves in high-speed jets. The origin of these waves, however, remains so far unexplained and a theory has yet to be developed. In the present study it will be shown that the computed wave patterns and propagation characteristics of the Kelvin-Helmholtz, the supersonic and the subsonic instability waves match essentially those observed by Oertel. The physical mechanisms which give rise to the three families of waves as well as some of the most salient characteristic features of each set of waves are discussed and reported here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 201 , April 1989 , pp. 447 - 483
Copyright
© 1989 Cambridge University Press

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