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The instability of inviscid jets and wakes in compressible fluid

Published online by Cambridge University Press:  28 March 2006

M. Lessen ,
J. A. Fox And  and
H. M. Zien
M. Lessen
Affiliation:
Department of Mechanical and Aerospace Sciences, The University of Rochester, Rochester, N.Y.
J. A. Fox And
Affiliation:
Department of Mechanical and Aerospace Sciences, The University of Rochester, Rochester, N.Y.
H. M. Zien
Affiliation:
Department of Mechanical and Aerospace Sciences, The University of Rochester, Rochester, N.Y.
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Abstract

The instability of a two-dimensional jet with respect to three-dimensional disturbances and that of an axially symmetric jet with respect to azimuthally periodic disturbances are studied, for the inviscid flow of a compressible fluid. In both cases the undisturbed velocity is assumed to be uniform in the jet. It is shown analytically that a two-dimensional jet is unstable under small disturbances, either subsonic or supersonic. There is no upper limit in Mach number, as was found for a plane vortex sheet, above which the flow is completely stable. Numerical calculations for the eigenvalues for both the two-dimensional jet and the axially symmetric jet have been made. The results indicate that the increase of Mach number tends to stabilize the flow. For the two-dimensional jet, the larger the angle between the direction of wave propagation and that of the main flow, the more the flow will be destabilized. For the axially symmetric jet, the flow is more unstable under azimuthally periodic disturbances than under rotationally symmetric ones, at small wave number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 1 , January 1965 , pp. 129 - 143
Copyright
© 1965 Cambridge University Press

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