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Formation of turbulent patterns near the onset of transition in plane Couette flow

Published online by Cambridge University Press:  22 March 2010

Y. DUGUET*
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-10044 Stockholm, Sweden LIMSI-CNRS, UPR 3251, 91403 Orsay, France
P. SCHLATTER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-10044 Stockholm, Sweden
D. S. HENNINGSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-10044 Stockholm, Sweden
*
Present address: LIMSI-CNRS, UPR 3251, Université Paris-Sud, 91403 Orsay, France. Email address for correspondence: duguet@mech.kth.se

Abstract

The formation of turbulent patterns in plane Couette flow is investigated near the onset of transition, using numerical simulation in a very large domain of size 800 h × 2 h × 356 h. Based on a maximum observation time of 20 000 inertial units, the threshold for the appearance of sustained turbulent motion is Rec = 324 ± 1. For Rec < Re ≤ 380, turbulent-banded patterns form, irrespective of whether the initial perturbation is a noise or localized disturbance. Measurements of the turbulent fraction versus Re show evidence for a discontinuous phase transition scenario where turbulent spots play the role of the nuclei. Using a smaller computational box, the angle selection of the turbulent bands in the early stages of their development is shown to be related to the amplitude of the initial perturbation.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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Duguet et al. supplementary movie

Movie 1. Streamwise velocity component in the mid-plane y=0, Re=320, starting from noise. All the turbulent spots eventually decay.

Download Duguet et al. supplementary movie(Video)
Video 7 MB

Duguet et al. supplementary movie

Movie 2. Streamwise velocity component in the mid-plane y=0, Re=350, starting from noise.

Download Duguet et al. supplementary movie(Video)
Video 9 MB

Duguet et al. supplementary movie

Movie 3. Streamwise velocity component in the mid-plane y=0, Re=350, starting from a localised initial perturbation

Download Duguet et al. supplementary movie(Video)
Video 10 MB