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).
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References
Craik, A.D.D. (1971) J.Fluid Mech, 50, 393–413
Kachanov, Y.S and Levchenko, V.Y. (1984) J.Fluid Mech, 138 209–47
Klebanoff, P.S, Tidstrom, K.D and Sargent, L.M (1962)
J. Fluid Mech, 12, 1–34 Smith, F.T. (1979) Proc.Roy.Soc.Lond., A366, 91–109
Smith, F.T. and Burggraff, O.D. (1985) Proc.Roy.Soc.Lond., A399, 25–55
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© 1990 Springer-Verlag Berlin Heidelberg
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Stewart, P.A. (1990). Three-Dimensional Effects in Boundary-Layer Transition: A High Reynolds Number Weakly-Nonlinear Theory. In: Arnal, D., Michel, R. (eds) Laminar-Turbulent Transition. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84103-3_13
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DOI: https://doi.org/10.1007/978-3-642-84103-3_13
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