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Stability of three-dimensional laminar and turbulent shear layers

Published online by Cambridge University Press:  29 March 2006

M. Lessen ,
G. Harpavat  and
H. M. Zien
M. Lessen
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester, Rochester, New York, 14627
G. Harpavat
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester, Rochester, New York, 14627
H. M. Zien
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester, Rochester, New York, 14627
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Abstract

The linear, normal mode instability of three-dimensional laminar and turbulent shear layers is studied. The flows consist of two streams semi-infinitely extended in the y-direction, flowing obliquely in the x-z plane. It is found that the stability of the flows depends on the main flow velocity components in the direction of the disturbance wave-number vector. Numerical calculations are performed to obtain the neutral stability curves. Under the usual parallel unperturbed flow assumption, the neutral stability curves pass through the origin of the α-R diagram, where α is the wave-number and R is the flow Reynolds number. It is also found that eddy viscosity has a destabilizing effect for small Reynolds numbers but a stabilizing effect at larger Reynolds numbers. Because any linear perturbation trajectory eventually leaves the unstable region of the α-R plane, it is probable that a Lin-Benney or Taylor-Goertler secondary instability ensues. Suitable components of the existing turbulence grow and develop into a large eddy system which causes rapid entrainment, giving rise to a turbulent burst. A first-order non-parallel correction is made to the neutral stability curves. The new curves have both upper and lower branches, and there exist minimum critical Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 39 - 59
Copyright
© 1969 Cambridge University Press

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References

Esch, R. E. 1957 J. Fluid Mech. 3, 289.
Lessen, M. 1950 NACA Rep. no. 979
Lessen, M. 1952 Quart. Appl. Math. 10, 184.
Liepman, W. H. & Laufer, J. 1947 NACA TN no. 1237.
Malkus, W. 1956 J. Fluid Mech. 1, 521.
Pai, S. I. 1954 Quart. Appl. Math. 12, 203.
Reynolds, W. C. & Tiederman, W. G. 1967 J. Fluid Mech. 27, 253.
Squire, H. B. 1933 Proc. Roy. Soc. A 142, no. A 847, Ser. A, 621.
Synge, J. L. 1938 Semi-centennial Publications of the American Mathematical Society, 2, 227.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1966 J. Fluid Mech. 26, 689.
Yamada, H. 1960 Rep. Res. Inst. Appl. Mech. 8, 30, 1.
Yamada, H. 1965 Rep. Res. Inst. Appl. Mech. 13, 45, 1.