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Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

Published online by Cambridge University Press:  06 April 2018

F. Alizard Open the ORCID record for F. Alizard [Opens in a new window] ,
A. Cadiou ,
L. Le Penven ,
B. Di Pierro  and
M. Buffat
F. Alizard*
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France DynFluid-CNAM, 151 Boulevard de l’Hôpital, 75013 Paris, France
A. Cadiou
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France
L. Le Penven
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France
B. Di Pierro
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France
M. Buffat
Affiliation:
LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, 43 Boulevard du 11 Novembre 1918, 69100 Villeurbanne, France
*
†Email address for correspondence: frederic.alizard@lecnam.net
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Abstract

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.

JFM classification

Boundary Layers: Boundary Layers Instability: Instability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 669 - 706
Copyright
© 2018 Cambridge University Press 

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