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On the nonlinear growth of single three-dimensional disturbances in boundary layers

Published online by Cambridge University Press:  26 February 2010

F. T. Smith ,
P. A. Stewart  and
R. G. A. Bowles
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
P. A. Stewart
Affiliation:
D.A.M.T.P., Silver Street, Cambridge, CB3 9EW
R. G. A. Bowles
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
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Summary

Experiments indicate the importance of three-dimensional action during transition, while high-Reynolds-number-flow theory indicates a multi-structured type of analysis. In line with this, the three-dimensional nonlinear unsteady triple-deck problem is addressed here, for slower transition. High-amplitude/high-frequency properties show enhanced disturbance growth occurring downstream for single nonlinear oblique waves inclined at angles greater than tan−1 √2 (≈54.7°) to the free stream, in certain interesting special cases. The three-dimensional response there is very ‘spiky’ and possibly random, with sideband instabilities present. A second nonlinear stage, and then an Euler stage, are entered further downstream, although faster transition can go straight into these more nonlinear stages. More general cases are also considered. Sideband effects, sublayer bursting and secondary instabilities are discussed, along with the relation to experimental observations.

Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 1 - 39
Copyright
Copyright © University College London 1994

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