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The growth of localized disturbances in a laminar boundary layer

Published online by Cambridge University Press:  28 March 2006

William O. Criminale  and
Leslie S. G. Kovasznay
William O. Criminale
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore
Leslie S. G. Kovasznay
Affiliation:
Department of Mechanics, The Johns Hopkins University, Baltimore Present address: Department of Mechanical Engineering, Princeton University, Princeton, New Jersey.
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Abstract

The classical theory of the instability of laminar flow predicts the growth (or decay) rate and phase velocity of two-dimensional small disturbance waves. In order to study the growth and dispersion of an originally localized spot-like disturbance, the initial disturbance is built up from all possible simple-harmonic waves. The propagation velocity and amplification rate for each vector wave-number then follows from the two-dimensional theory by Squire's generalization. The initial development can be solved explicitly by a power series in time, and the asymptotic behaviour is also predicted. For times between initial and final periods, exact numerical calculations have been made using an IBM 709 electronic computer. The role which localized disturbances can play in ultimate transition to turbulent motion is also indicated.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 1 , September 1962 , pp. 59 - 80
Copyright
© 1962 Cambridge University Press

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