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Boundary-layer transition by interaction of discrete and continuous modes

Published online by Cambridge University Press:  14 May 2008

YANG LIU ,
TAMER A. ZAKI  and
PAUL A. DURBIN
YANG LIU
Affiliation:
Mechanical Engineering, Stanford University, CA 94305, USA
TAMER A. ZAKI
Affiliation:
Mechanical Engineering, Imperial College London, SW7 2AZ, UK
PAUL A. DURBIN
Affiliation:
Aerospace Engineering, Iowa State University, IA 50011, USA
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Abstract

The natural and bypass routes to boundary-layer turbulence have traditionally been studied independently. In certain flow regimes, both transition mechanisms might coexist, and, if so, can interact. A nonlinear interaction of discrete and continuous Orr-Sommerfeld modes, which are at the origin of orderly and bypass transition, respectively, is found. It causes breakdown to turbulence, even though neither mode alone is sufficient. Direct numerical simulations of the interaction shows that breakdown occurs through a pattern of Λ-structures, similar to the secondary instability of Tollmien–Schlichting waves. However, the streaks produced by the Orr-Sommerfeld continuous mode set the spanwise length scale, which is much smaller than that of the secondary instability of Tollmien–Schlichting waves. Floquet analysis explains some of the features seen in the simulations as a competition between destabilizing and stabilizing interactions between finite-amplitude distortions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 604 , 10 June 2008 , pp. 199 - 233
Copyright
Copyright © Cambridge University Press 2008

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