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Transient disturbance growth in a corrugated channel

Published online by Cambridge University Press:  10 November 2006

J. SZUMBARSKI  and
J. M. FLORYAN
J. SZUMBARSKI
Affiliation:
Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, Warsaw, Poland, 00-665
J. M. FLORYAN
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A5B9, Canada
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Abstract

Transient growth of small disturbances may lead to the initiation of the laminar–turbulent transition process. Such growth in a two-dimensional laminar flow in a channel with a corrugated wall is analysed. The corrugation has a wavy form that is completely characterized by its wavenumber and amplitude. The maximum possible growth and the form of the initial disturbance that leads to such growth have been identified for each form of the corrugation. The form that leads to the largest growth for a given corrugation amplitude, i.e. the optimal corrugation, has been found. It is shown that the corrugation acts as an amplifier for disturbances that are approximately optimal in the smooth channel case but has little effect in the other cases. The interplay between the modal (asymptotic) instability and the transient growth, and the use of the variable corrugation for modulation of the growth are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 568 , 10 December 2006 , pp. 243 - 272
Copyright
© 2006 Cambridge University Press

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