Three-Dimensional Effects in Boundary-Layer Transition: A High Reynolds Number Weakly-Nonlinear Theory

  • P. A. Stewart
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

We are concerned here with the development of Tollmien-Schlichting (T-S) waves in an incompressible flat-plate boundary-layer. Suppose that a small-amplitude 2-D T-S wave of frequency ω *. is introduced by a vibrating ribbon. It decays up to the lower-branch neutral position x0, and subsequently grows. If the initial amplitude is not too small, nonlinear effects then come into play, and the disturbance acquires significant three-dimensionality. This may take the form of a roughly-periodic spanwise variation of T-S amplitude (“peak-valley splitting”), together with the formation of a mean longditudinal-vortex system, as in the experiments of Klebanoff et al (1962). On the other hand, for lower disturbance amplitudes, the dominant three-dimensional components may be subharmonics of the primary 2-D wave — e.g. Kachanov and Levchenko (1984).

Keywords

Vortex Triad 

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References

  1. Craik, A.D.D. (1971) J.Fluid Mech, 50, 393–413ADSMATHCrossRefGoogle Scholar
  2. Kachanov, Y.S and Levchenko, V.Y. (1984) J.Fluid Mech, 138 209–47ADSCrossRefGoogle Scholar
  3. Klebanoff, P.S, Tidstrom, K.D and Sargent, L.M (1962)Google Scholar
  4. J. Fluid Mech, 12, 1–34 Smith, F.T. (1979) Proc.Roy.Soc.Lond., A366, 91–109CrossRefGoogle Scholar
  5. Smith, F.T. and Burggraff, O.D. (1985) Proc.Roy.Soc.Lond., A399, 25–55ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • P. A. Stewart
    • 1
  1. 1.Department of MathematicsUniversity College LondonUK

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