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On shear-layer instability, breakdown and transition

Published online by Cambridge University Press:  28 March 2006

H. P. Greenspan  and
D. J. Benney
H. P. Greenspan
Affiliation:
Mathematics Department, Massachusetts Institute of Technology
D. J. Benney
Affiliation:
Mathematics Department, Massachusetts Institute of Technology
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Abstract

The problem of the linear stability of a time-dependent shear flow is investigated and the effects of contraction and expansion of the layer are discussed. Models of flows observed prior to breakdown are constructed and used to investigate the resulting secondary instabilities which are shown to be extremely violent and in essential agreement with recent experiments. In relatively short time, one half period of the primary oscillation, the energy in the secondary disturbance increases by two orders of magnitude; the wave-number corresponding to maximum amplification is five times that of the primary wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 15 , Issue 1 , January 1963 , pp. 133 - 153
Copyright
© 1963 Cambridge University Press

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References

Benney, D. J. 1961 J. Fluid Mech. 10, 209.
Benney, D. J. & Lin, C. C. 1960 Phys. Fluids, 3, 656.
Carrier, G. F. 1954 Los Alamos Internal Report.
Esch, R. E. 1957 J. Fluid Mech. 3, 289.
Klebanoff, P. D., Tidstrom, D. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Report: The Johns Hopkins University, Baltimore.
Lin, C. C. 1945 Parts I, II, III. Quart. Appl. Math. 3, 117, 218, 277.
Lin, C. C. 1955 Hydrodynamic Stability. Cambridge University Press.
Schubauer, G. B. 1957 Boundary Layer Research Symposium, p. 85. Freiburg.
Schubauer, G. B. & Skramstead, H. K. 1948 Nat. Adv. Comm. Aero., Wash., Report, no. 909.
Sato, H. & Kuriki, K. 1961 J. Fluid Mech. 11, 321.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Watson, J. 1960 J. Fluid Mech. 9, 371.