Letter | Published:

The rise of fully turbulent flow

Nature volume 526, pages 550553 (22 October 2015) | Download Citation

Abstract

Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow1,2,3,4,5,6. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence7 and fully turbulent flows8,9.

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Acknowledgements

We thank A. P. Willis for sharing his hybrid spectral finite-difference code, and X. Tu for helping to set up and test the experiment. We acknowledge the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. B.S. acknowledges financial support from the Chinese State Scholarship Fund under grant number 2010629145. B.S. acknowledges support from the International Max Planck Research School for the Physics of Biological and Complex Systems and the Göttingen Graduate School for Neurosciences and Molecular Biosciences. We acknowledge computing resources from GWDG (Gesellschaft für wissenschaftliche Datenverarbeitung Göttingen) and the Jülich Supercomputing Centre (grant HGU16) where the simulations were performed.

Author information

Affiliations

  1. Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

    • Dwight Barkley
  2. IST Austria, 3400 Klosterneuburg, Austria

    • Baofang Song
    • , Vasudevan Mukund
    • , Grégoire Lemoult
    •  & Björn Hof
  3. Max Planck Institute for Dynamics and Self-Organization, Bunsenstrasse 10, 37073 Göttingen, Germany

    • Baofang Song
  4. Institute for Multiscale Simulation, Friedrich-Alexander-Universität, 91052 Erlangen, Germany

    • Baofang Song
  5. Institute of Fluid Mechanics, Friedrich-Alexander-Universität, 91058 Erlangen, Germany

    • Marc Avila

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Contributions

V.M., G.L. and B.H. designed and performed the experiments and analysed the experimental results. B.S. and M.A. designed and performed the computer simulations of the Navier–Stokes equations. B.S., M.A. and B.H. analysed the numerical results. B.S. generated the corresponding visualizations. D.B. performed the theoretical analysis. D.B., B.S., V.M., G.L., M.A. and B.H. wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Dwight Barkley or Björn Hof.

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https://doi.org/10.1038/nature15701

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