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A model for subharmonic resonance within wavepackets in unstable boundary layers

Published online by Cambridge University Press:  22 June 2001

A. D. D. CRAIK
A. D. D. CRAIK
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, UK
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Abstract

In recent experiments on the growth of localized disturbances in a Blasius boundary layer, Medeiros & Gaster (1999a, b) observed that the development of nonlinear effects depends markedly on the initial phase of their imposed disturbance. Here, a simple explanation of this phenomenon is proposed. Because the disturbance is localized in space and time, it has a spread of wavenumbers and frequencies: among these are components which can initiate a pair of resonant subharmonic waves with well-determined phase, which are then amplified by the familiar three-wave resonance mechanism. The amplitude attained after some time is strongly phase-dependent, consistent with the experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 432 , 10 April 2001 , pp. 409 - 418
Copyright
© 2001 Cambridge University Press

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