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On an active resonant triad of mixed modes in symmetric shear flows: a plane wake as a paradigm

Published online by Cambridge University Press:  26 April 2006

Xuesong Wu
Xuesong Wu
Affiliation:
Department of Mathematics, Imperial College, 180 Queens Gate, London SW7 2BZ, UK
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Abstract

In this paper, we identify a new type of resonant triad which operates in a parallel or nearly parallel shear flow with a symmetric profile. The triad consists of a planar sinuous mode, an oblique sinuous mode and an oblique varicose mode, but is not of the usual subharmonic-resonance form. The development of the triad is studied in the non-equilibrium critical-layer régime. The equations governing the evolution of the modes are derived. We show that the quadratic resonance can significantly enhance the growth of both the oblique sinuous and varicose modes, and may cause them to grow super-exponentially. This can lead to a subsequent stage in which the oblique sinuous mode produces a back reaction on the oblique varicose mode through a phase-locked interaction, causing both oblique modes to evolve even more rapidly. We suggest that the resonant triad is a viable mechanism for the development of three-dimensional structures and varicose components observed in the later stage of plane wake transition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 317 , 25 June 1996 , pp. 337 - 368
Copyright
© 1996 Cambridge University Press

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