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A note on spatially growing three-dimensional disturbances in a free shear layer

Published online by Cambridge University Press:  29 March 2006

A. Michalke
Affiliation:
Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt e.V., Institut für Turbulenzforschung, Berlin

Abstract

It does not seem to be possible to prove analytically that an incompressible, inviscid free shear layer is less unstable with respect to spatially growing three-dimensional disturbances than to two-dimensional ones. For this reason a numerical calculation for the special case of the hyperbolic tangent velocity profile was performed. It was found that even for spatially growing disturbances the amplification of three-dimensional disturbances is smaller than for two-dimensional ones.

Type
Research Article
Copyright
© 1969 Cambridge University Press

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References

Al'Tschuler, L. V. 1965 Uspekhi 8, 52.
Bernstein, I. B., Frieman, E. A., Kruskal, M. D. & Kulsrud, R. M. 1958 Proc. Roy. Soc. A, 244, 17.
Birkhoff, G. 1956 Los Alamos Scientific Laboratory Report LA 1927.
Cesari, L. 1963 Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations. Berlin: Springer.
Champetier, J.-L., Larger, J.-C., Lechanche, Y. & Nelson, P. 1965 C. R. Acad. Sci., Paris. 261, 2825.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Cotsaftis, M. 1968 J. Inst. Maths. Applics. 5, 19.
Di Gregorio, C., Herlach, F. & Knoepfel, H. 1966 Proc. Conf. on Megagauss Magnetic Field Generation by Explosives and Related Experiments, Frascati 1965. Brussels: EURATOM 2750e.
Emmons, H. W., Chang, C. T. & Watson, B. C. 1960 J. Fluid Mech. 7, 177.
Guerri, L. & Stella, P. EURATOM Ispra. (To be published.)
Harlow, F. H. & Welch, J. E. 1966 Phys. Fluids 9, 842.
Harris, E. G. 1962 Phys. Fluids 5, 1057.
Hartman, P. 1964 Ordinary Differential Equations. New York: Wiley.
Jarem, J. & Watson, M. 1962 Proc. Vth Int. Conf. on Ionization Phenomena in Gases, Munich. Amsterdam: North Holland.
Kruskal, M. & Schwarzschild, M. 1954 Proc. Roy. Soc. A, 223, 348.
Lehner, G., Linhart, J. G. & Somon, J. P. 1964 Nuclear Fusion 4, 362.
Liapounoff, M. A. 1949 Probléms général de la stabilité du mouvement. Princeton University Press.
Linhart, J. G. 1961 J. Appl. Phys. 32, 500.
Plesset, M. S. 1954 J. Appl. Phys. 25, 96.
Rayleigh, J. W. S. 1900 Scientific Papers, vol. II. Cambridge University Press.
Somon, J. P. 1966 Proc. Conf. on Megagauss Magnetic Field Generation by Explosives and Related Experiments, Frascati 1965. Brussells: EURATOM 2750e.
Somon, J. P. 1968a Laboratori Gas Ionizzati Report LGI 68/4.
Somon, J. P. 1968b Sur l'obtention de champs magnétiques intenses au moyen d'une implosion cylindrique. Thèse de Doctorat és Sciences, Euratom Report EUR 4197f.
Taylor, G. 1950 Proc. Roy. Soc. A, 201, 192.
Wehausen, J. V. & Laitone, E. V. 1960 Encyclopedia of Physics, vol. III. Fluid Dynamics. Berlin: Springer.