Shear layer instability of an inviscid compressible fluid. Part 2

Author:

Blumen W.,Drazin P. G.,Billings D. F.

Abstract

The linear stability of a shear layer of an inviscid compressible fluid is considered. It is shown that there is instability of two-dimensional disturbances at all values of the Mach number, contrary to previous results for a vortex sheet. The difference arises from the discovery of a second unstable mode. This mode is supersonic, decays weakly with distance from the shear layer, and is not governed by the principle of exchange of stabilities. Detailed numerical and asymptotic results are given for the hyperbolic-tangent shear layer.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference15 articles.

1. Dickinson, R. E. & Clare, F. J. 1973 Numerical study of the unstable modes of a hyperbolic-tangent barotropic shear flow.J. Atmos. Sci. 30,1035–1049.

2. Lin, C. C. 1953 On the stability of the laminar mixing region between two parallel streams in a gas. N.A.C.A. Tech. Note , no. 2887.

3. Liepmann, H. W. & Puckett, A. E. 1947 Introduction to Aerodynamics of a Compressible Fluid .Wiley.

4. Howe, M. S. 1970 Transmission of an acoustic pulse through a plane vortex sheet.J. Fluid Mech. 43,353–367.

5. Blumen, W. 1975 Stability of non-planar shear flow of a stratified fluid.J. Fluid Mech. 68,177–189.

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