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Shear layer instability of an inviscid compressible fluid. Part 2

Published online by Cambridge University Press:  29 March 2006

W. Blumen ,
P. G. Drazin  and
D. F. Billings
W. Blumen
Affiliation:
Department of Astro-Geophysics, University of Colorado, Boulder
P. G. Drazin
Affiliation:
School of Mathematics, University of Bristol, England
D. F. Billings
Affiliation:
Department of Aerospace Sciences, University of Colorado, Boulder
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 2 , 23 September 1975 , pp. 305 - 316
Copyright
© 1975 Cambridge University Press

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References

Banks, W. H. H. & Drazin, P. G. 1973 Perturbation methods in boundary-layer theory. J. Fluid Mech. 58, 763–775.Google Scholar
Blumen, W. 1970 Shear layer instability of an inviscid compressible fluid. J. Fluid Mech. 40, 769–781.Google Scholar
Blumen, W. 1975 Stability of non-planar shear flow of a stratified fluid. J. Fluid Mech. 68, 177–189.Google Scholar
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.Google Scholar
Drazin, P. G. 1958 The stability of a shear layer in an unbounded heterogeneous inviscid fluid. J. Fluid Mech. 4, 214–224.Google Scholar
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of inviscid fluid. Adv. in Appl. Mech. 9, 1–89.Google Scholar
Dunn, D. W. & Lin, C. C. 1952 The stability of the laminar boundary layer in a compressible fluid for the case of three-dimensional disturbances. J. Aero. Sci. 19, 491.Google Scholar
Fejer, J. A. & Miles, J. W. 1963 On the stability of a plane vortex sheet with respect to three-dimensional disturbances. J. Fluid Mech. 15, 335–336.Google Scholar
Gill, A. E. & Drazin, P. G. 1965 Note on instability of compressible jets and wakes to long-wave disturbances. J. Fluid Mech. 22, 415.Google Scholar
Hatanaka, H. 1947 On the stability of a surface of discontinuity in a compressible fluid. J. Soc. Sci. Culture, Japan, 2, 3–7.Google Scholar
Howe, M. S. 1970 Transmission of an acoustic pulse through a plane vortex sheet. J. Fluid Mech. 43, 353–367.Google Scholar
Huppert, H. E. 1973 On Howard's technique for perturbing neutral solutions of the Taylor-Goldstein equation. J. Fluid Mech. 57, 361–368.Google Scholar
Landau, L. 1944 Stability of tangential discontinuities in compressible fluid. Akad. Nauk. S.S.S.R., Comptes Rendus (Doklady), 44, 139–141.Google Scholar
Liepmann, H. W. & Puckett, A. E. 1947 Introduction to Aerodynamics of a Compressible Fluid. Wiley.
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.