---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21295'
abstract:
- lang: eng
text: 'Depending on the type of flow, the transition to turbulence can take one
of two forms: either turbulence arises from a sequence of instabilities or from
the spatial proliferation of transiently chaotic domains, a process analogous
to directed percolation. The former scenario is commonly referred to as a supercritical
transition and frequently encountered in flows destabilized by body forces, whereas
the latter subcritical transition is common in shear flows. Both cases are inherently
continuous in a sense that the transformation from ordered laminar to fully turbulent
fluid motion is only accomplished gradually with flow speed. Here we show that
these established transition types do not account for the more general setting
of shear flows subject to body forces. The combination of the two continuous scenarios
leads to the attenuation of spatial coupling; with increasing forcing amplitude,
the transition becomes increasingly sharp and eventually discontinuous. We argue
that the suppression of laminar–turbulent coexistence and the approach towards
a discontinuous phase transition potentially apply to a broad range of situations
including flows subject to, for example, buoyancy, centrifugal or electromagnetic
forces.'
acknowledgement: The work was supported by the Simons Foundation (grant number 662960,
to B.H.). Open access funding provided by Institute of Science and Technology (IST
Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Bowen
full_name: Yang, Bowen
id: 71b6ff4b-15b2-11ec-abd3-aef6b028cf7e
last_name: Yang
orcid: 0000-0002-4843-6853
- first_name: Yi
full_name: Zhuang, Yi
id: 3677B57C-F248-11E8-B48F-1D18A9856A87
last_name: Zhuang
- first_name: Gökhan
full_name: Yalniz, Gökhan
id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
last_name: Yalniz
orcid: 0000-0002-8490-9312
- first_name: Mukund
full_name: Vasudevan, Mukund
id: 3C5A959A-F248-11E8-B48F-1D18A9856A87
last_name: Vasudevan
- first_name: Elena
full_name: Marensi, Elena
id: 0BE7553A-1004-11EA-B805-18983DDC885E
last_name: Marensi
orcid: 0000-0001-7173-4923
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Yang B, Zhuang Y, Yalniz G, Vasudevan M, Marensi E, Hof B. Discontinuous transition
to shear flow turbulence. Nature Physics. 2026;22:424-429. doi:10.1038/s41567-025-03166-3
apa: Yang, B., Zhuang, Y., Yalniz, G., Vasudevan, M., Marensi, E., & Hof, B.
(2026). Discontinuous transition to shear flow turbulence. Nature Physics.
Springer Nature. https://doi.org/10.1038/s41567-025-03166-3
chicago: Yang, Bowen, Yi Zhuang, Gökhan Yalniz, Mukund Vasudevan, Elena Marensi,
and Björn Hof. “Discontinuous Transition to Shear Flow Turbulence.” Nature
Physics. Springer Nature, 2026. https://doi.org/10.1038/s41567-025-03166-3.
ieee: B. Yang, Y. Zhuang, G. Yalniz, M. Vasudevan, E. Marensi, and B. Hof, “Discontinuous
transition to shear flow turbulence,” Nature Physics, vol. 22. Springer
Nature, pp. 424–429, 2026.
ista: Yang B, Zhuang Y, Yalniz G, Vasudevan M, Marensi E, Hof B. 2026. Discontinuous
transition to shear flow turbulence. Nature Physics. 22, 424–429.
mla: Yang, Bowen, et al. “Discontinuous Transition to Shear Flow Turbulence.” Nature
Physics, vol. 22, Springer Nature, 2026, pp. 424–29, doi:10.1038/s41567-025-03166-3.
short: B. Yang, Y. Zhuang, G. Yalniz, M. Vasudevan, E. Marensi, B. Hof, Nature Physics
22 (2026) 424–429.
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: Source data are available via Zenodo at https://doi.org/10.5281/zenodo.17514317
(ref. 51). The numerical simulations were carried out using the open-source codes
openpipeflow41 and nsPipeflow45.
date_created: 2026-02-17T11:38:41Z
date_published: 2026-03-01T00:00:00Z
date_updated: 2026-07-27T11:13:48Z
day: '01'
ddc:
- '532'
department:
- _id: GradSch
- _id: BjHo
doi: 10.1038/s41567-025-03166-3
external_id:
arxiv:
- '2311.11474'
file:
- access_level: open_access
checksum: 0636abba74896c467a7237411fa2369b
content_type: application/pdf
creator: dernst
date_created: 2026-07-27T11:12:46Z
date_updated: 2026-07-27T11:12:46Z
file_id: '22420'
file_name: 2026_NaturePhysics_Yang.pdf
file_size: 5152735
relation: main_file
success: 1
file_date_updated: 2026-07-27T11:12:46Z
has_accepted_license: '1'
intvolume: ' 22'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Published Version
page: 424-429
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'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Discontinuous transition to shear flow turbulence
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2026'
...
---
APC_amount: 7068 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20402'
abstract:
- lang: eng
text: The recent classification of the onset of turbulence as a directed percolation
(DP) phase transition has been applied to all major shear flows including pipe,
channel, Couette and boundary layer flows. A cornerstone of the DP analogy is
the memoryless (Poisson) property of turbulent sites. We here show that, for the
classic case of channel flow, neither the decay nor the proliferation of turbulent
stripes is memoryless. As demonstrated by a standard analysis of the respective
survival curves, isolated channel stripes, in the immediate vicinity of the critical
point, age. Consequently, the one to one mapping between turbulent stripes and
active DP-sites is not fulfilled in this low Reynolds number regime. In addition,
the interpretation of turbulence as a chaotic saddle with supertransient properties,
the basis of recent theoretical progress, does not apply to individual localized
stripes. The discrepancy between channel flow and the transition models established
for pipe and Couette flow, illustrates that seemingly minor geometrical differences
between flows can give rise to instabilities and growth mechanisms that fundamentally
alter the nature of the transition to turbulence.
acknowledgement: This work was supported by a grant from the Simons Foundation (662960,
BH). We thank Yohann Duguet for helpful discussions, Baofang Song for the initial
adaptation of openpipeflow57 to the channel geometry, and Ashley P. Willis for openpipeflow57.
article_number: '8447'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Mukund
full_name: Vasudevan, Mukund
id: 3C5A959A-F248-11E8-B48F-1D18A9856A87
last_name: Vasudevan
- first_name: Chaitanya S
full_name: Paranjape, Chaitanya S
id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87
last_name: Paranjape
- first_name: Michael Philip
full_name: Sitte, Michael Philip
id: 0ba0f1f2-9cfe-11f0-bee6-f95318d225b0
last_name: Sitte
- first_name: Gökhan
full_name: Yalniz, Gökhan
id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
last_name: Yalniz
orcid: 0000-0002-8490-9312
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. Aging and memory of transitional
turbulence. Nature Communications. 2025;16. doi:10.1038/s41467-025-63044-7
apa: Vasudevan, M., Paranjape, C. S., Sitte, M. P., Yalniz, G., & Hof, B. (2025).
Aging and memory of transitional turbulence. Nature Communications. Springer
Nature. https://doi.org/10.1038/s41467-025-63044-7
chicago: Vasudevan, Mukund, Chaitanya S Paranjape, Michael Philip Sitte, Gökhan
Yalniz, and Björn Hof. “Aging and Memory of Transitional Turbulence.” Nature
Communications. Springer Nature, 2025. https://doi.org/10.1038/s41467-025-63044-7.
ieee: M. Vasudevan, C. S. Paranjape, M. P. Sitte, G. Yalniz, and B. Hof, “Aging
and memory of transitional turbulence,” Nature Communications, vol. 16.
Springer Nature, 2025.
ista: Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. 2025. Aging and memory
of transitional turbulence. Nature Communications. 16, 8447.
mla: Vasudevan, Mukund, et al. “Aging and Memory of Transitional Turbulence.” Nature
Communications, vol. 16, 8447, Springer Nature, 2025, doi:10.1038/s41467-025-63044-7.
short: M. Vasudevan, C.S. Paranjape, M.P. Sitte, G. Yalniz, B. Hof, Nature Communications
16 (2025).
corr_author: '1'
date_created: 2025-09-27T13:27:31Z
date_published: 2025-09-26T00:00:00Z
date_updated: 2026-05-20T07:56:59Z
day: '26'
ddc:
- '532'
department:
- _id: BjHo
doi: 10.1038/s41467-025-63044-7
external_id:
arxiv:
- '2112.06537'
isi:
- '001582555200041'
file:
- access_level: open_access
checksum: 945926ead9cde464435d456427e2869e
content_type: application/pdf
creator: gyalniz
date_created: 2025-09-27T13:32:03Z
date_updated: 2025-09-27T13:32:03Z
file_id: '20403'
file_name: s41467-025-63044-7.pdf
file_size: 2226082
relation: main_file
file_date_updated: 2025-09-27T13:32:03Z
has_accepted_license: '1'
intvolume: ' 16'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 238598C6-32DE-11EA-91FC-C7463DDC885E
grant_number: '662960'
name: Revisiting the Turbulence Problem Using Statistical Mechanics
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Nature Communications
publication_identifier:
eissn:
- 2041-1723
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Aging and memory of transitional turbulence
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2025'
...
---
_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. Nature Physics. 2024;20:1339-1345.
doi:10.1038/s41567-024-02513-0
apa: Lemoult, G. M., Vasudevan, M., Shih, H. Y., Linga, G., Mathiesen, J., Goldenfeld,
N., & Hof, B. (2024). Directed percolation and puff jamming near the transition
to pipe turbulence. Nature Physics. Springer Nature. https://doi.org/10.1038/s41567-024-02513-0
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.” Nature Physics. Springer Nature,
2024. https://doi.org/10.1038/s41567-024-02513-0.
ieee: G. M. Lemoult et al., “Directed percolation and puff jamming near the
transition to pipe turbulence,” Nature Physics, 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.” Nature Physics, vol. 20, Springer Nature,
2024, pp. 1339–45, doi:10.1038/s41567-024-02513-0.
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'
...
---
OA_place: repository
OA_type: green
_id: '5996'
abstract:
- lang: eng
text: 'In pipes, turbulence sets in despite the linear stability of the laminar
Hagen–Poiseuille flow. The Reynolds number ( ) for which turbulence first appears
in a given experiment – the ‘natural transition point’ – depends on imperfections
of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations.
At onset, turbulence typically only occupies a certain fraction of the flow, and
this fraction equally is found to differ from experiment to experiment. Despite
these findings, Reynolds proposed that after sufficiently long times, flows may
settle to steady conditions: below a critical velocity, flows should (regardless
of initial conditions) always return to laminar, while above this velocity, eddying
motion should persist. As will be shown, even in pipes several thousand diameters
long, the spatio-temporal intermittent flow patterns observed at the end of the
pipe strongly depend on the initial conditions, and there is no indication that
different flow patterns would eventually settle to a (statistical) steady state.
Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless),
we continuously recreate the puff sequence exiting the pipe at the pipe entrance,
and in doing so introduce periodic boundary conditions for the puff pattern. This
procedure allows us to study the evolution of the flow patterns for arbitrary
long times, and we find that after times in excess of advective time units, indeed
a statistical steady state is reached. Although the resulting flows remain spatio-temporally
intermittent, puff splitting and decay rates eventually reach a balance, so that
the turbulent fraction fluctuates around a well-defined level which only depends
on . In accordance with Reynolds’ proposition, we find that at lower (here 2020),
flows eventually always resume to laminar, while for higher ( ), turbulence persists.
The critical point for pipe flow hence falls in the interval of $2020 , which
is in very good agreement with the recently proposed value of . The latter estimate
was based on single-puff statistics and entirely neglected puff interactions.
Unlike in typical contact processes where such interactions strongly affect the
percolation threshold, in pipe flow, the critical point is only marginally influenced.
Interactions, on the other hand, are responsible for the approach to the statistical
steady state. As shown, they strongly affect the resulting flow patterns, where
they cause ‘puff clustering’, and these regions of large puff densities are observed
to travel across the puff pattern in a wave-like fashion.'
acknowledged_ssus:
- _id: M-Shop
acknowledgement: ' We also thank Philipp Maier and the IST Austria workshop for their
dedicated technical support'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mukund
full_name: Vasudevan, Mukund
id: 3C5A959A-F248-11E8-B48F-1D18A9856A87
last_name: Vasudevan
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Vasudevan M, Hof B. The critical point of the transition to turbulence in pipe
flow. Journal of Fluid Mechanics. 2018;839:76-94. doi:10.1017/jfm.2017.923
apa: Vasudevan, M., & Hof, B. (2018). The critical point of the transition to
turbulence in pipe flow. Journal of Fluid Mechanics. Cambridge University
Press. https://doi.org/10.1017/jfm.2017.923
chicago: Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition
to Turbulence in Pipe Flow.” Journal of Fluid Mechanics. Cambridge University
Press, 2018. https://doi.org/10.1017/jfm.2017.923.
ieee: M. Vasudevan and B. Hof, “The critical point of the transition to turbulence
in pipe flow,” Journal of Fluid Mechanics, vol. 839. Cambridge University
Press, pp. 76–94, 2018.
ista: Vasudevan M, Hof B. 2018. The critical point of the transition to turbulence
in pipe flow. Journal of Fluid Mechanics. 839, 76–94.
mla: Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition to
Turbulence in Pipe Flow.” Journal of Fluid Mechanics, vol. 839, Cambridge
University Press, 2018, pp. 76–94, doi:10.1017/jfm.2017.923.
short: M. Vasudevan, B. Hof, Journal of Fluid Mechanics 839 (2018) 76–94.
corr_author: '1'
date_created: 2019-02-14T12:50:50Z
date_published: 2018-03-25T00:00:00Z
date_updated: 2026-07-28T14:02:09Z
day: '25'
department:
- _id: BjHo
doi: 10.1017/jfm.2017.923
ec_funded: 1
external_id:
arxiv:
- '1709.06372'
isi:
- '000437858300003'
intvolume: ' 839'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.06372
month: '03'
oa: 1
oa_version: Preprint
page: 76-94
project:
- _id: 25152F3A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '306589'
name: Decoding the complexity of turbulence at its origin
publication: Journal of Fluid Mechanics
publication_identifier:
eissn:
- 1469-7645
issn:
- 0022-1120
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The critical point of the transition to turbulence in pipe flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 839
year: '2018'
...
---
_id: '1664'
abstract:
- lang: eng
text: 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 flow. 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 turbulence and fully turbulent flows.
acknowledgement: 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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Dwight
full_name: Barkley, Dwight
last_name: Barkley
- first_name: Baofang
full_name: Song, Baofang
last_name: Song
- first_name: Mukund
full_name: Vasudevan, Mukund
id: 3C5A959A-F248-11E8-B48F-1D18A9856A87
last_name: Vasudevan
- first_name: Grégoire M
full_name: Lemoult, Grégoire M
id: 4787FE80-F248-11E8-B48F-1D18A9856A87
last_name: Lemoult
- 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: Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. The rise of fully
turbulent flow. Nature. 2015;526(7574):550-553. doi:10.1038/nature15701
apa: Barkley, D., Song, B., Vasudevan, M., Lemoult, G. M., Avila, M., & Hof,
B. (2015). The rise of fully turbulent flow. Nature. Nature Publishing
Group. https://doi.org/10.1038/nature15701
chicago: Barkley, Dwight, Baofang Song, Mukund Vasudevan, Grégoire M Lemoult, Marc
Avila, and Björn Hof. “The Rise of Fully Turbulent Flow.” Nature. Nature
Publishing Group, 2015. https://doi.org/10.1038/nature15701.
ieee: D. Barkley, B. Song, M. Vasudevan, G. M. Lemoult, M. Avila, and B. Hof, “The
rise of fully turbulent flow,” Nature, vol. 526, no. 7574. Nature Publishing
Group, pp. 550–553, 2015.
ista: Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. 2015. The rise
of fully turbulent flow. Nature. 526(7574), 550–553.
mla: Barkley, Dwight, et al. “The Rise of Fully Turbulent Flow.” Nature,
vol. 526, no. 7574, Nature Publishing Group, 2015, pp. 550–53, doi:10.1038/nature15701.
short: D. Barkley, B. Song, M. Vasudevan, G.M. Lemoult, M. Avila, B. Hof, Nature
526 (2015) 550–553.
corr_author: '1'
date_created: 2018-12-11T11:53:20Z
date_published: 2015-10-21T00:00:00Z
date_updated: 2025-09-23T14:15:52Z
day: '21'
department:
- _id: BjHo
doi: 10.1038/nature15701
ec_funded: 1
external_id:
arxiv:
- '1510.09143'
isi:
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intvolume: ' 526'
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issue: '7574'
language:
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main_file_link:
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url: http://arxiv.org/abs/1510.09143
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oa_version: Preprint
page: 550 - 553
project:
- _id: 25152F3A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '306589'
name: Decoding the complexity of turbulence at its origin
publication: Nature
publication_status: published
publisher: Nature Publishing Group
publist_id: '5485'
quality_controlled: '1'
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status: public
title: The rise of fully turbulent flow
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 526
year: '2015'
...