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On the instability of a three-dimensional attachment-line boundary layer: weakly nonlinear theory and a numerical approach

Published online by Cambridge University Press:  21 April 2006

Philip Hall  and
Mujeeb R. Malik
Philip Hall
Affiliation:
Mathematics Department, University of Exeter, North Park Road, Exeter, England
Mujeeb R. Malik
Affiliation:
High Technology Corporation, Hampton, VA 23666
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Abstract

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier–Stokes equations for the attachment-line flow have been solved using a Fourier–Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 257 - 282
Copyright
© 1986 Cambridge University Press

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References

Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia.
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 Proc. R. Soc. Lond. A 395, 229.
Herbert, T. 1977 In Laminar—Turbulent Transition, AOARD Conf. Proc. No. 224, p. 31.
Hooking, L. M. 1974 Quart. J. Mech. Appl. Math. 28, 341.
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1984 NASA Contractor Rep. no. 172365, ICASE Report no. 84–19.
Moin, P. & Kim, J. 1982 J. Fluid Mech. 118, 341.
Orszag, S. A. & Kells, L. C. 1980 J. Fluid Mech. 96, 159.
Pfenninger, W. & Bacon, J. W. 1969 In Viscous Drag Reduction (ed. C. S. Wells), p. 85. Plenum Press.
Poll, D. I. A. 1979 Aero. Quart. 30, 607.
Poll, D. I. A. 1980 IUTAM Symposium on Laminar—Turbulent Transition. Springer.
Stewartson, K. & Stuart, J. T. 1971 J. Fluid Mech. 48, 529.