---
_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.'
acknowledgement: ' We also thank Philipp Maier and the IST Austria workshop for theirdedicated
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.
date_created: 2019-02-14T12:50:50Z
date_published: 2018-03-25T00:00:00Z
date_updated: 2023-09-19T14:37:49Z
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
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.
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.
date_created: 2018-12-11T11:53:20Z
date_published: 2015-10-21T00:00:00Z
date_updated: 2021-01-12T06:52:22Z
day: '21'
department:
- _id: BjHo
doi: 10.1038/nature15701
ec_funded: 1
intvolume: ' 526'
issue: '7574'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1510.09143
month: '10'
oa: 1
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'
scopus_import: 1
status: public
title: The rise of fully turbulent flow
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 526
year: '2015'
...