---
_id: '17128'
abstract:
- lang: eng
  text: The onset of turbulence in pipe flow has defied detailed understanding ever
    since the first observations of the spatially heterogeneous nature of the transition.
    Recent theoretical studies and experiments in simpler, shear-driven flows suggest
    that the onset of turbulence is a directed-percolation non-equilibrium phase transition,
    but whether these findings are generic and also apply to open or pressure-driven
    flows is unknown. In pipe flow, the extremely long time scales near the transition
    make direct observations of critical behaviour virtually impossible. Here we find
    a technical solution to that limitation and show that the universality class of
    the transition is directed percolation, from which a jammed phase of puffs emerges
    above the critical point. Our method is to experimentally characterize all pairwise
    interactions between localized patches of turbulence puffs and use these interactions
    as input for renormalization group and computer simulations of minimal models
    that extrapolate to long length and time scales. The strong interactions in the
    jamming regime enable us to explicitly measure the turbulent fraction and confirm
    model predictions. Our work shows that directed-percolation scaling applies beyond
    simple closed shear flows and underscores how statistical mechanics can lead to
    profound, quantitative and predictive insights on turbulent flows and their phases.
acknowledgement: We gratefully acknowledge the assistance of J. M. Lopez with DNSs
  at an early stage of this work. This work was partially supported by two grants
  from the Simons Foundation (grant nos. 662985 (N.G.) and 662960 (B.H.)) and by Ministry
  of Science and Technology, Taiwan (grant nos. MOST 109-2112-M-001-017-MY3 and MOST
  111-2112-M-001-027-MY3 (H.-Y.S.)). Part of this work was performed using computing
  resources of CRIANN (Normandy, France).
article_processing_charge: No
article_type: original
author:
- first_name: Grégoire M
  full_name: Lemoult, Grégoire M
  id: 4787FE80-F248-11E8-B48F-1D18A9856A87
  last_name: Lemoult
- first_name: Mukund
  full_name: Vasudevan, Mukund
  id: 3C5A959A-F248-11E8-B48F-1D18A9856A87
  last_name: Vasudevan
- first_name: Hong Yan
  full_name: Shih, Hong Yan
  last_name: Shih
- first_name: Gaute
  full_name: Linga, Gaute
  last_name: Linga
- first_name: Joachim
  full_name: Mathiesen, Joachim
  last_name: Mathiesen
- first_name: Nigel
  full_name: Goldenfeld, Nigel
  last_name: Goldenfeld
- 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, Vasudevan M, Shih HY, et al. Directed percolation and puff jamming
    near the transition to pipe turbulence. <i>Nature Physics</i>. 2024;20:1339-1345.
    doi:<a href="https://doi.org/10.1038/s41567-024-02513-0">10.1038/s41567-024-02513-0</a>
  apa: Lemoult, G. M., Vasudevan, M., Shih, H. Y., Linga, G., Mathiesen, J., Goldenfeld,
    N., &#38; Hof, B. (2024). Directed percolation and puff jamming near the transition
    to pipe turbulence. <i>Nature Physics</i>. Springer Nature. <a href="https://doi.org/10.1038/s41567-024-02513-0">https://doi.org/10.1038/s41567-024-02513-0</a>
  chicago: Lemoult, Grégoire M, Mukund Vasudevan, Hong Yan Shih, Gaute Linga, Joachim
    Mathiesen, Nigel Goldenfeld, and Björn Hof. “Directed Percolation and Puff Jamming
    near the Transition to Pipe Turbulence.” <i>Nature Physics</i>. Springer Nature,
    2024. <a href="https://doi.org/10.1038/s41567-024-02513-0">https://doi.org/10.1038/s41567-024-02513-0</a>.
  ieee: G. M. Lemoult <i>et al.</i>, “Directed percolation and puff jamming near the
    transition to pipe turbulence,” <i>Nature Physics</i>, vol. 20. Springer Nature,
    pp. 1339–1345, 2024.
  ista: Lemoult GM, Vasudevan M, Shih HY, Linga G, Mathiesen J, Goldenfeld N, Hof
    B. 2024. Directed percolation and puff jamming near the transition to pipe turbulence.
    Nature Physics. 20, 1339–1345.
  mla: Lemoult, Grégoire M., et al. “Directed Percolation and Puff Jamming near the
    Transition to Pipe Turbulence.” <i>Nature Physics</i>, vol. 20, Springer Nature,
    2024, pp. 1339–45, doi:<a href="https://doi.org/10.1038/s41567-024-02513-0">10.1038/s41567-024-02513-0</a>.
  short: G.M. Lemoult, M. Vasudevan, H.Y. Shih, G. Linga, J. Mathiesen, N. Goldenfeld,
    B. Hof, Nature Physics 20 (2024) 1339–1345.
corr_author: '1'
date_created: 2024-06-09T22:01:03Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T07:50:20Z
day: '01'
department:
- _id: BjHo
doi: 10.1038/s41567-024-02513-0
external_id:
  isi:
  - '001232300600001'
intvolume: '        20'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
page: 1339-1345
project:
- _id: 238598C6-32DE-11EA-91FC-C7463DDC885E
  grant_number: '662960'
  name: Revisiting the Turbulence Problem Using Statistical Mechanics
publication: Nature Physics
publication_identifier:
  eissn:
  - 1745-2481
  issn:
  - 1745-2473
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Directed percolation and puff jamming near the transition to pipe turbulence
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 20
year: '2024'
...