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Weakly nonlinear stability of a viscous free shear layer

Published online by Cambridge University Press:  11 April 2006

S. A. Maslowe
S. A. Maslowe
Affiliation:
Department of Mathematics, McGill University, Montreal, Quebec, Canada
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Abstract

Numerical calculations of the Landau constant are presented for the case of a shear layer of finite Reynolds number, having the velocity profile $\overline{u} = \tan h\,y$. It is found that this parameter has a strong dependence on the Reynolds number for Re [les ] 100. In particular, the Landau constant is reduced by 43% from its inviscid value when Re = 40, the latter value being typical of many experiments. This percentage, however, is based upon a calculation in which the mean-flow distortion has been neglected. A rough estimate of the latter effect indicates that it could possibly increase the value of the Landau constant sufficiently that the net influence of a finite Reynolds number would be of a smaller magnitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 4 , 23 March 1977 , pp. 689 - 702
Copyright
© 1977 Cambridge University Press

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References

Benney, D. J. 1961 J. Fluid Mech. 10, 209.
Benney, D. J. & Maslowe, S. A. 1975 Stud. Appl. Math. 54, 181.
Betchov, R. & Szewczyk, A. 1963 Phys. Fluids, 6, 1391.
Browand, F. 1966 J. Fluid Mech. 26, 281.
Browand, F. & Winant, C. 1973 Boundary-Layer Met. 5, 67.
Davey, A. 1973 Quart. J. Mech. Appl. Math. 26, 401.
Freymuth, P. 1966 J. Fluid Mech. 25, 683.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Michalke, A. 1964 J. Fluid Mech. 19, 543.
Miksad, R. W. 1972 J. Fluid Mech. 56, 695.
Patnaik, P., Sherman, F. & Corcos, G. 1976 J. Fluid Mech. 73, 215.
Schade, H. 1964 Phys. Fluids, 7, 623.
Scotti, R. S. & Corcos, G. M. 1972 J. Fluid Mech. 52, 499.
Shanks, D. 1955 J. Math. & Phys. 34, 1.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Stuart, J. T. 1967 J. Fluid Mech. 29, 417.
Thomas, J. H. 1953 Phys. Rev. 91, 780.
Ting, L. 1959 J. Math. & Phys. 38, 153.
Watson, J. 1960 J. Fluid Mech. 9, 371.