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The radiation of sound by the instability waves of a compressible plane turbulent shear layer

Published online by Cambridge University Press:  19 April 2006

Christopher K. W. Tam  and
Philip J. Morris
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Philip J. Morris
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
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Abstract

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near-and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 349 - 381
Copyright
© 1980 Cambridge University Press

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