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Edge states for the turbulence transition in the asymptotic suction boundary layer

Published online by Cambridge University Press:  30 May 2013

Tobias Kreilos ,
Gregor Veble ,
Tobias M. Schneider  and
Bruno Eckhardt
Tobias Kreilos*
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany
Gregor Veble
Affiliation:
Pipistrel d.o.o. Ajdovščina, Goriška c. 50a, SI-5270 Ajdovščina, Slovenia University of Nova Gorica, Vipavska 13, SI-5000 Nova Gorica, Slovenia
Tobias M. Schneider
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA
Bruno Eckhardt
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany J. M. Burgerscentrum, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
*
†Email address for correspondence: tobias.kreilos@physik.uni-marburg.de
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Abstract

We demonstrate the existence of an exact invariant solution to the Navier–Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream-oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer, we demonstrate that the periodic orbit emerges in a saddle–node infinite-period (SNIPER) bifurcation of two symmetry-related travelling-wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability, which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.

JFM classification

Boundary Layers: Boundary Layers Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 100 - 122
Copyright
©2013 Cambridge University Press 

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