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Edge states as mediators of bypass transition in boundary-layer flows

Published online by Cambridge University Press:  21 July 2016

T. Khapko ,
T. Kreilos ,
P. Schlatter ,
Y. Duguet ,
B. Eckhardt  and
D. S. Henningson
T. Khapko
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), SE-100 44 Stockholm, Sweden
T. Kreilos
Affiliation:
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
P. Schlatter*
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), SE-100 44 Stockholm, Sweden
Y. Duguet
Affiliation:
LIMSI, CNRS, Université Paris-Saclay, F-91405 Orsay, France
B. Eckhardt
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany J. M. Burgerscentrum, Delft University of Technology, NL-2628 CD Delft, The Netherlands
D. S. Henningson
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Swedish e-Science Research Centre (SeRC), SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: pschlatt@mech.kth.se
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Abstract

The concept of edge states is investigated in the asymptotic suction boundary layer in relation to the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge state plays the role of state-space mediator.

JFM classification

Boundary Layers: Boundary Layers Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , R2
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Copyright
© 2016 Cambridge University Press 

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Khapko et al. supplementary movie

Three-dimensional animation of the edge state developing as a function of time; the edge state is reached after t=7000. The movie corresponds to an animated version of Figure 2, however with higher isolevels of both velocity fluctuations and λ2 (corresponding to the ones in Figure 5).

Download Khapko et al. supplementary movie(Video)
Video 4 MB

Khapko et al. supplementary movie

State-space view of noise-induced transition. The movie corresponds to an animated version of Figure 6.

Download Khapko et al. supplementary movie(Video)
Video 2 MB