Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T03:44:13.189Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  22 March 2010

Y. DUGUET ,
P. SCHLATTER  and
D. S. HENNINGSON
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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 119 - 129
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent-laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.CrossRefGoogle ScholarPubMed
Barkley, D. & Tuckerman, L. S. 2007 Mean flow of turbulent laminar patterns in plane Couette flow. J. Fluid Mech. 576, 109–137.CrossRefGoogle Scholar
Binder, K. 1987 Theory of first-order phase transitions. Rep. Prog. Phys. 50, 783–859.CrossRefGoogle Scholar
Bottin, S. & Chaté, H. 1998 Statistical analysis of the transition to turbulence in plane Couette flow. Eur. Phys. J. B 6, 143–155.Google Scholar
Bottin, S., Daviaud, F., Manneville, P. & Dauchot, O. 1998 a Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43, 171–176.CrossRefGoogle Scholar
Bottin, S., Dauchot, O., Daviaud, F. & Manneville, P. 1998 b Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow. Phys. Fluids 10, 2597–2607.Google Scholar
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007 A pseudo-spectral solver for incompressible boundary layer flows. Tech. rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Colovas, P. W. & Andereck, C. D. 1997 Turbulent bursting and spatiotemporal intermittency in the counter-rotating Taylor–Couette system. Phys. Rev. E 55, 2736.CrossRefGoogle Scholar
Dauchot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335–343.Google Scholar
Daviaud, F., Hegseth, J. J. & Berg, P. 1992 Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69, 2511–2514.Google Scholar
Duguet, Y., Schlatter, P. & Henningson, D. S. 2009 Localized edge states in plane Couette flow. Phys. Fluids 21, 111701.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech 287, 317–348.CrossRefGoogle Scholar
Hegseth, J. J. 1996 Turbulent spots in plane Couette flow. Phys. Rev. E 5, 4915.CrossRefGoogle Scholar
Imry, Y. 1980 Finite-size rounding of a first-order phase transition. Phys. Rev. B 5, 2042–2043.Google Scholar
Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259.Google Scholar
Lagha, M. & Manneville, P. 2007 Modeling transitional plane Couette flow. Eur. Phys. J. B 58, 433–447.Google Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.Google Scholar
Manneville, P. 2005 Modeling the direct transition to turbulence. In Laminar-Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R. R.), Springer.Google Scholar
Manneville, P. 2009 Spatiotemporal perspective on the decay of turbulence Phys. Rev. E 79, 025301.Google Scholar
Pomeau, Y. 1986 Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23, 3–11.Google Scholar
Prigent, A. 2003 La spirale turbulente: motif de grande longueur d'onde dans les écoulements cisaillés turbulents. PhD thesis, Université Paris XI, Paris.Google Scholar
Prigent, A., Grégoire, G., Chaté, H., Dauchot, O. & Van Saarlos, W. 2002 Large-scale finite-wavelength modulation within turbulent shear flows. Phys. Rev. Lett. 89, 014501.Google Scholar
Romanov, V. A. 1973 Stability of plane-parallel Couette flow. Funct. Anal. Appl. 7, 137–146.Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.CrossRefGoogle Scholar
Van Atta, C. W. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.Google Scholar
Yochelis, A., Hagberg, A., Meron, E., Lin, A. L. & Swinney, H. L. 2002 Development of standing-wave labyrinthine patterns. SIADS 2, 236–247.Google Scholar

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 6.5 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 9.5 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