Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T07:11:41.770Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient states in plane Couette flow

Published online by Cambridge University Press:  30 September 2020

D. De Souza ,
T. Bergier  and
R. Monchaux Open the ORCID record for R. Monchaux [Opens in a new window]
D. De Souza
Affiliation:
IMSIA UMR 9219, ENSTA-Paris, CNRS, CEA, EDF, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91762Palaiseau CEDEX, France
T. Bergier
Affiliation:
IMSIA UMR 9219, ENSTA-Paris, CNRS, CEA, EDF, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91762Palaiseau CEDEX, France
R. Monchaux*
Affiliation:
IMSIA UMR 9219, ENSTA-Paris, CNRS, CEA, EDF, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91762Palaiseau CEDEX, France
*
†Email address for correspondence: monchaux@ensta.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the rich and complex relaxation dynamics of turbulent plane Couette flow when the Reynolds number is lowered. In particular, we reveal the existence of well-defined transient states around which the dynamics of turbulent retreat is organized. We characterize these states in physical space and we propose a projection of these states in phase space to understand their nature. The results presented have been obtained in an experiment in which we perform annealing and quenching, i.e. gentle or sudden decreases in Reynolds number. The nature of asymptotic states is also studied and shown to depend on the final Reynolds number, but not at all on the rate of change of the Reynolds number.

JFM classification

Instability: Transition to turbulence Nonlinear Dynamical Systems: Pattern formation Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A33
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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

van Atta, C. 1966 Exporatory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.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.CrossRefGoogle Scholar
Bottin, S., Daviaud, F., Manneville, P. & Dauchot, O. 1998 Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43, 171–176.CrossRefGoogle Scholar
Brand, E. & Gibson, J. F. 2014 A doubly localized equilibrium solution of plane Couette flow. J. Fluid Mech. 750, R3.CrossRefGoogle Scholar
Budanur, N. B. & Hof, B. 2017 Heteroclinic path to spatially localized chaos in pipe flow. J. Fluid Mech. 827, R1.CrossRefGoogle Scholar
Chantry, M., Tuckerman, L. S. & Barkley, D. 2017 Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech. 824.CrossRefGoogle Scholar
Coles, D. 1962 Interfaces and intermittency in turbulent shear flow. In Mecanique de la Turbulence, Marseille, 28 August to 2 September, pp. 229–250. CNRS.Google Scholar
Couliou, M. & Monchaux, R. 2015 Large-scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism. Phys. Fluids 27 (3), 034101.CrossRefGoogle Scholar
Couliou, M. & Monchaux, R. 2016 Spreading of turbulence in plane Couette flow. Phys. Rev. E 93 (1), 013108.CrossRefGoogle ScholarPubMed
Couliou, M. & Monchaux, R. 2017 Growth dynamics of turbulent spots in plane Couette flow. J. Fluid Mech. 819, 1–20.CrossRefGoogle Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.CrossRefGoogle Scholar
Dauchot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335–343.CrossRefGoogle Scholar
De Lozar, A., Mellibovsky, F, Avila, M & Hof, B. 2012 Edge state in pipe flow experiments. Phys. Rev. Lett. 108 (21), 214502.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Duguet, Y. & Schlatter, P. 2013 Oblique laminar–turbulent interfaces in plane shear flows. Phys. Rev. Lett. 110 (3), 034502.CrossRefGoogle ScholarPubMed
Duguet, Y., Schlatter, P. & Henningson, D. S. 2009 Localized edge states in plane Couette flow. Phys. Fluids 21, 111701.CrossRefGoogle Scholar
Duguet, Y., Schlatter, P. & Henningson, D. S. 2010 Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119.CrossRefGoogle Scholar
Emmons, H. W. & Bryson, A. E. 1951 The laminar–turbulent transition in a boundary layer. Tans. ASME J. Appl. Mech. 18, 331–331.Google Scholar
Gibson, J. F., Halcrow, J. & Cvitanovic, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107–130.CrossRefGoogle Scholar
Haralick, R. M., Sternberg, S. R. & Zhuang, X. 1987 Image analysis using mathematical morphology. IEEE Trans. Pattern Anal. Mach. Intell. 9 (4), 532–550.CrossRefGoogle ScholarPubMed
Itano, T. & Toh, S. 2001 The dynamics of bursting process in wall turbulence. J. Phys. Soc. Japan 70, 703.CrossRefGoogle Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Klotz, L. & Wesfreid, J. E. 2017 Experiments on transient growth of turbulent spots. J. Fluid Mech. 829.CrossRefGoogle Scholar
Lagha, M. & Manneville, P. 2007 Modeling of plane Couette flow. I. Large scale flow around turbulent spots. Phys. Fluids 19 (9), 094105.CrossRefGoogle Scholar
Lemoult, G., Aider, J.-L. & Wesfreid, J.-E. 2013 Turbulent spots in a channel: large-scale flow and self-sustainability. J. Fluid Mech. 731, R1.CrossRefGoogle Scholar
Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B. 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254–258.CrossRefGoogle Scholar
Manneville, P. 2011 On the decay of turbulence in plane Couette flow. Fluid Dyn. Res. 43 (6), 065501.CrossRefGoogle Scholar
Manneville, P. 2012 On the growth of laminar–turbulent patterns in plane Couette flow. Fluid Dyn. Res. 44 (3), 031412.CrossRefGoogle Scholar
Manneville, P. 2015 On the transition to turbulence of wall-bounded flows in general and plane Couette flow in particular. Eur. J. Mech.-B/Fluids 49, 345–362.CrossRefGoogle Scholar
Moisy, F. 2020 Pivmat Toolbox for Matlab. Available at: http://www.fast.u-psud.fr/pivmat/.Google Scholar
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96 (9), 094501.CrossRefGoogle ScholarPubMed
Philip, J. & Manneville, P. 2011 From temporal to spatiotemporal dynamics in transitional plane Couette flow. Phys. Rev. E 83 (3), 036308.CrossRefGoogle ScholarPubMed
Pomeau, Y. 1986 Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23, 3–11.CrossRefGoogle Scholar
Prigent, A. & Dauchot, O. 2005 Transition to versus from turbulence in subcritical Couette flows. In IUATM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions (ed. T. Mullin & R. Kerswell), pp. 195–219. Springer.CrossRefGoogle Scholar
Quénot, G. M., Pakleza, J. & Kowalewski, T. A. 1998 Particle image velocimetry with optical flow. Exp. Fluids 25 (3), 177–189.Google Scholar
Reetz, F., Kreilos, T. & Schneider, T. M. 2019 Exact invariant solution reveals the origin of self-organized oblique turbulent–laminar stripes. Nat. Commun. 10 (1), 1–6.CrossRefGoogle ScholarPubMed
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12 (3), 249.CrossRefGoogle Scholar
Schmiegel, A. & Eckhardt, B. 2000 Persistent turbulence in annealed plane Couette flow. Europhys. Lett. 51 (4), 395.CrossRefGoogle Scholar
Schneider, T. M., Eckhardt, B. & Yorke, J. A. 2007 Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett. 99 (3), 034502.CrossRefGoogle ScholarPubMed
Skufca, J. D., Yorke, J. A. & Eckhardt, B. 2006 Edge of chaos in a parallel shear flow. Phys. Rev. Lett. 96 (17), 174101.CrossRefGoogle Scholar
Trefethen, L., Trefethen, A., Reddy, S. & Driscoll, T. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578–584.CrossRefGoogle ScholarPubMed
Tsukahara, T., Kawaguchi, Y., Kawamura, H., Tillmark, N. & Alfredsson, P. H. 2010 Turbulence stripe in transitional channel flow with/without system rotation. In Seventh IUTAM Symposium on Laminar-Turbulent Transition (ed. P. Schlatter & D. S. Henningson), p. 421. Springer.CrossRefGoogle Scholar
Tuckerman, L. S., Chantry, M. & Barkley, D. 2020 Patterns in wall-bounded shear flows. Annu. Rev. Fluid Mech. 52, 343–67.CrossRefGoogle Scholar
Wang, Z., Guet, C., Monchaux, R., Duguet, Y. & Eckhardt, B. 2020 Quadrupolar flows around spots in internal shear flows. J. Fluid Mech. 892, A27.CrossRefGoogle Scholar
Willis, A. P. & Kerswell, R. R. 2008 Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states. J. Fluid Mech. 619, 213.CrossRefGoogle Scholar