---
_id: '1494'
abstract:
- lang: eng
  text: Turbulence is one of the most frequently encountered non-equilibrium phenomena
    in nature, yet characterizing the transition that gives rise to turbulence in
    basic shear flows has remained an elusive task. Although, in recent studies, critical
    points marking the onset of sustained turbulence have been determined for several
    such flows, the physical nature of the transition could not be fully explained.
    In extensive experimental and computational studies we show for the example of
    Couette flow that the onset of turbulence is a second-order phase transition and
    falls into the directed percolation universality class. Consequently, the complex
    laminar–turbulent patterns distinctive for the onset of turbulence in shear flows
    result from short-range interactions of turbulent domains and are characterized
    by universal critical exponents. More generally, our study demonstrates that even
    high-dimensional systems far from equilibrium such as turbulence exhibit universality
    at onset and that here the collective dynamics obeys simple rules.
acknowledgement: We thank P. Maier for providing valuable ideas and supporting us
  in the technical aspects. Discussions with D. Barkley, Y. Duguet, B. Eckhart, N.
  Goldenfeld, P. Manneville and K. Takeuchi are gratefully acknowledged. 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. L.S. and B.H. acknowledge research
  funding by Deutsche Forschungsgemeinschaft (DFG) under Grant No. SFB 963/1 (project
  A8). Numerical simulations were performed thanks to the CPU time allocations of
  JUROPA in Juelich Supercomputing Center (project HGU17) and of the Max Planck Computing
  and Data Facility (Garching, Germany). Excellent technical support from M. Rampp
  on the hybrid code nsCouette is appreciated.
author:
- first_name: Grégoire M
  full_name: Lemoult, Grégoire M
  id: 4787FE80-F248-11E8-B48F-1D18A9856A87
  last_name: Lemoult
- first_name: Liang
  full_name: Shi, Liang
  id: 374A3F1A-F248-11E8-B48F-1D18A9856A87
  last_name: Shi
- first_name: Kerstin
  full_name: Avila, Kerstin
  last_name: Avila
- first_name: Shreyas V
  full_name: Jalikop, Shreyas V
  id: 44A1D772-F248-11E8-B48F-1D18A9856A87
  last_name: Jalikop
- first_name: Marc
  full_name: Avila, Marc
  last_name: Avila
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
citation:
  ama: Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. Directed percolation
    phase transition to sustained turbulence in Couette flow. <i>Nature Physics</i>.
    2016;12(3):254-258. doi:<a href="https://doi.org/10.1038/nphys3675">10.1038/nphys3675</a>
  apa: Lemoult, G. M., Shi, L., Avila, K., Jalikop, S. V., Avila, M., &#38; Hof, B.
    (2016). Directed percolation phase transition to sustained turbulence in Couette
    flow. <i>Nature Physics</i>. Nature Publishing Group. <a href="https://doi.org/10.1038/nphys3675">https://doi.org/10.1038/nphys3675</a>
  chicago: Lemoult, Grégoire M, Liang Shi, Kerstin Avila, Shreyas V Jalikop, Marc
    Avila, and Björn Hof. “Directed Percolation Phase Transition to Sustained Turbulence
    in Couette Flow.” <i>Nature Physics</i>. Nature Publishing Group, 2016. <a href="https://doi.org/10.1038/nphys3675">https://doi.org/10.1038/nphys3675</a>.
  ieee: G. M. Lemoult, L. Shi, K. Avila, S. V. Jalikop, M. Avila, and B. Hof, “Directed
    percolation phase transition to sustained turbulence in Couette flow,” <i>Nature
    Physics</i>, vol. 12, no. 3. Nature Publishing Group, pp. 254–258, 2016.
  ista: Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. 2016. Directed percolation
    phase transition to sustained turbulence in Couette flow. Nature Physics. 12(3),
    254–258.
  mla: Lemoult, Grégoire M., et al. “Directed Percolation Phase Transition to Sustained
    Turbulence in Couette Flow.” <i>Nature Physics</i>, vol. 12, no. 3, Nature Publishing
    Group, 2016, pp. 254–58, doi:<a href="https://doi.org/10.1038/nphys3675">10.1038/nphys3675</a>.
  short: G.M. Lemoult, L. Shi, K. Avila, S.V. Jalikop, M. Avila, B. Hof, Nature Physics
    12 (2016) 254–258.
date_created: 2018-12-11T11:52:21Z
date_published: 2016-02-15T00:00:00Z
date_updated: 2021-01-12T06:51:08Z
day: '15'
department:
- _id: BjHo
doi: 10.1038/nphys3675
ec_funded: 1
intvolume: '        12'
issue: '3'
language:
- iso: eng
month: '02'
oa_version: None
page: 254 - 258
project:
- _id: 25152F3A-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '306589'
  name: Decoding the complexity of turbulence at its origin
- _id: 2511D90C-B435-11E9-9278-68D0E5697425
  grant_number: SFB 963  TP A8
  name: Astrophysical instability of currents and turbulences
publication: Nature Physics
publication_status: published
publisher: Nature Publishing Group
publist_id: '5685'
quality_controlled: '1'
scopus_import: 1
status: public
title: Directed percolation phase transition to sustained turbulence in Couette flow
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2016'
...