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Mathematical Problems in Engineering
Volume 5 (1999), Issue 4, Pages 317-328
http://dx.doi.org/10.1155/S1024123X99001118

Vortex formation and stability analysis for shear flows over combined spatially and temporally structured walls

Department of Theoretical and Applied Mechanics, 216 Talbot Laboratory, University of Illinois at Urbana-Champaign, 104 S. Wright Street, Urbana 61801, IL, USA

Received 24 June 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Benney's theory of evolution of disturbances in shear flows over smooth and flat boundary is extended to study for shear flows over combined spatially and temporally corrugated walls. Perturbation and multiple-scales analyses are employed for the case where both amplitude of the corrugations and the amplitude of wave motion are small. Analyses for instability of modulated mean shear flows with respect to spanwise-periodic disturbance rolls and for the subsequent vortex formation and vortex stability are presented, and the effects of the corrugated walls on the resulting flow and vortices are determined. It is found that particular corrugated walls can originate and control the longitudinal vortices, while some other types of corrugated walls can enhance instability of such vortices.