---
_id: '13274'
abstract:
- lang: eng
text: Viscous flows through pipes and channels are steady and ordered until, with
increasing velocity, the laminar motion catastrophically breaks down and gives
way to turbulence. How this apparently discontinuous change from low- to high-dimensional
motion can be rationalized within the framework of the Navier-Stokes equations
is not well understood. Exploiting geometrical properties of transitional channel
flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible
and identify the complete path that reversibly links fully turbulent motion to
an invariant solution. This precursor of turbulence destabilizes rapidly with
Re, and the accompanying explosive increase in attractor dimension effectively
marks the transition between deterministic and de facto stochastic dynamics.
acknowledgement: We thank Baofang Song as well as the developers of Channelflow for
sharing their numerical codes, and Mukund Vasudevan and Holger Kantz for fruitful
discussions. This work was supported by a grant from the Simons Foundation (662960,
B. H.).
article_number: '034002'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chaitanya S
full_name: Paranjape, Chaitanya S
id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87
last_name: Paranjape
- first_name: Gökhan
full_name: Yalniz, Gökhan
id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
last_name: Yalniz
orcid: 0000-0002-8490-9312
- first_name: Yohann
full_name: Duguet, Yohann
last_name: Duguet
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. Direct path from turbulence
to time-periodic solutions. Physical Review Letters. 2023;131(3). doi:10.1103/physrevlett.131.034002
apa: Paranjape, C. S., Yalniz, G., Duguet, Y., Budanur, N. B., & Hof, B. (2023).
Direct path from turbulence to time-periodic solutions. Physical Review Letters.
American Physical Society. https://doi.org/10.1103/physrevlett.131.034002
chicago: Paranjape, Chaitanya S, Gökhan Yalniz, Yohann Duguet, Nazmi B Budanur,
and Björn Hof. “Direct Path from Turbulence to Time-Periodic Solutions.” Physical
Review Letters. American Physical Society, 2023. https://doi.org/10.1103/physrevlett.131.034002.
ieee: C. S. Paranjape, G. Yalniz, Y. Duguet, N. B. Budanur, and B. Hof, “Direct
path from turbulence to time-periodic solutions,” Physical Review Letters,
vol. 131, no. 3. American Physical Society, 2023.
ista: Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. 2023. Direct path from
turbulence to time-periodic solutions. Physical Review Letters. 131(3), 034002.
mla: Paranjape, Chaitanya S., et al. “Direct Path from Turbulence to Time-Periodic
Solutions.” Physical Review Letters, vol. 131, no. 3, 034002, American
Physical Society, 2023, doi:10.1103/physrevlett.131.034002.
short: C.S. Paranjape, G. Yalniz, Y. Duguet, N.B. Budanur, B. Hof, Physical Review
Letters 131 (2023).
date_created: 2023-07-24T09:43:59Z
date_published: 2023-07-21T00:00:00Z
date_updated: 2023-12-13T11:40:19Z
day: '21'
department:
- _id: GradSch
- _id: BjHo
doi: 10.1103/physrevlett.131.034002
external_id:
arxiv:
- '2306.05098'
isi:
- '001052929900004'
intvolume: ' 131'
isi: 1
issue: '3'
keyword:
- General Physics and Astronomy
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.05098
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 238598C6-32DE-11EA-91FC-C7463DDC885E
grant_number: '662960'
name: 'Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental
Studies on Transitional and Turbulent Flows'
publication: Physical Review Letters
publication_identifier:
eissn:
- 1079-7114
issn:
- 0031-9007
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
status: public
title: Direct path from turbulence to time-periodic solutions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 131
year: '2023'
...
---
_id: '8043'
abstract:
- lang: eng
text: With decreasing Reynolds number, Re, turbulence in channel flow becomes spatio-temporally
intermittent and self-organises into solitary stripes oblique to the mean flow
direction. We report here the existence of localised nonlinear travelling wave
solutions of the Navier–Stokes equations possessing this obliqueness property.
Such solutions are identified numerically using edge tracking coupled with arclength
continuation. All solutions emerge in saddle-node bifurcations at values of Re
lower than the non-localised solutions. Relative periodic orbit solutions bifurcating
from branches of travelling waves have also been computed. A complete parametric
study is performed, including their stability, the investigation of their large-scale
flow, and the robustness to changes of the numerical domain.
acknowledgement: The authors thank S. Zammert and B. Budanur for useful discussions.
J. F. Gibson is gratefully acknowledged for the development and the maintenance
of the code Channelflow. Y.D. would like to thank P. Schlatter and D. S. Henningson
for an early collaboration on a similar topic in the case of plane Couette flow
during the years 2008–2013.
article_number: A7
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Chaitanya S
full_name: Paranjape, Chaitanya S
id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87
last_name: Paranjape
- first_name: Yohann
full_name: Duguet, Yohann
last_name: Duguet
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
citation:
ama: Paranjape CS, Duguet Y, Hof B. Oblique stripe solutions of channel flow. Journal
of Fluid Mechanics. 2020;897. doi:10.1017/jfm.2020.322
apa: Paranjape, C. S., Duguet, Y., & Hof, B. (2020). Oblique stripe solutions
of channel flow. Journal of Fluid Mechanics. Cambridge University Press.
https://doi.org/10.1017/jfm.2020.322
chicago: Paranjape, Chaitanya S, Yohann Duguet, and Björn Hof. “Oblique Stripe Solutions
of Channel Flow.” Journal of Fluid Mechanics. Cambridge University Press,
2020. https://doi.org/10.1017/jfm.2020.322.
ieee: C. S. Paranjape, Y. Duguet, and B. Hof, “Oblique stripe solutions of channel
flow,” Journal of Fluid Mechanics, vol. 897. Cambridge University Press,
2020.
ista: Paranjape CS, Duguet Y, Hof B. 2020. Oblique stripe solutions of channel flow.
Journal of Fluid Mechanics. 897, A7.
mla: Paranjape, Chaitanya S., et al. “Oblique Stripe Solutions of Channel Flow.”
Journal of Fluid Mechanics, vol. 897, A7, Cambridge University Press, 2020,
doi:10.1017/jfm.2020.322.
short: C.S. Paranjape, Y. Duguet, B. Hof, Journal of Fluid Mechanics 897 (2020).
date_created: 2020-06-29T07:59:35Z
date_published: 2020-08-25T00:00:00Z
date_updated: 2023-08-22T07:48:02Z
day: '25'
ddc:
- '530'
department:
- _id: BjHo
doi: 10.1017/jfm.2020.322
external_id:
isi:
- '000539132300001'
file:
- access_level: open_access
checksum: 3f487bf6d9286787096306eaa18702e8
content_type: application/pdf
creator: cziletti
date_created: 2020-06-30T08:37:37Z
date_updated: 2020-07-14T12:48:08Z
file_id: '8070'
file_name: 2020_JournalOfFluidMech_Paranjape.pdf
file_size: 767873
relation: main_file
file_date_updated: 2020-07-14T12:48:08Z
has_accepted_license: '1'
intvolume: ' 897'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Fluid Mechanics
publication_identifier:
eissn:
- '14697645'
issn:
- '00221120'
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Oblique stripe solutions of channel flow
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 897
year: '2020'
...
---
_id: '6957'
abstract:
- lang: eng
text: "In many shear flows like pipe flow, plane Couette flow, plane Poiseuille
flow, etc. turbulence emerges subcritically. Here, when subjected to strong enough
perturbations, the flow becomes turbulent in spite of the laminar base flow being
linearly stable. The nature of this instability has puzzled the scientific community
for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally
intermittent. In pipe flow the localized turbulent structures are referred to
as puffs and in planar flows like plane Couette and channel flow, patches arise
in the form of localized oblique bands. In this thesis, we study the onset of
turbulence in channel flow in direct numerical simulations from a dynamical system
theory perspective, as well as by performing experiments in a large aspect ratio
channel.\r\n\r\nThe aim of the experimental work is to determine the critical
Reynolds number where turbulence first becomes sustained. Recently, the onset
of turbulence has been described in analogy to absorbing state phase transition
(i.e. directed percolation). In particular, it has been shown that the critical
point can be estimated from the competition between spreading and decay processes.
Here, by performing experiments, we identify the mechanisms underlying turbulence
proliferation in channel flow and find the critical Reynolds number, above which
turbulence becomes sustained. Above the critical point, the continuous growth
at the tip of the stripes outweighs the stochastic shedding of turbulent patches
at the tail and the stripes expand. For growing stripes, the probability to decay
decreases while the probability of stripe splitting increases. Consequently, and
unlike for the puffs in pipe flow, neither of these two processes is time-independent
i.e. memoryless. Coupling between stripe expansion and creation of new stripes
via splitting leads to a significantly lower critical point ($Re_c=670+/-10$)
than most earlier studies suggest. \r\n\r\nWhile the above approach sheds light
on how turbulence first becomes sustained, it provides no insight into the origin
of the stripes themselves. In the numerical part of the thesis we investigate
how turbulent stripes form from invariant solutions of the Navier-Stokes equations.
The origin of these turbulent stripes can be identified by applying concepts from
the dynamical system theory. In doing so, we identify the exact coherent structures
underlying stripes and their bifurcations and how they give rise to the turbulent
attractor in phase space. We first report a family of localized nonlinear traveling
wave solutions of the Navier-Stokes equations in channel flow. These solutions
show structural similarities with turbulent stripes in experiments like obliqueness,
quasi-streamwise streaks and vortices, etc. A parametric study of these traveling
wave solution is performed, with parameters like Reynolds number, stripe tilt
angle and domain size, including the stability of the solutions. These solutions
emerge through saddle-node bifurcations and form a phase space skeleton for the
turbulent stripes observed in the experiments. The lower branches of these TW
solutions at different tilt angles undergo Hopf bifurcation and new solutions
branches of relative periodic orbits emerge. These RPO solutions do not belong
to the same family and therefore the routes to chaos for different angles are
different. \r\n\r\nIn shear flows, turbulence at onset is transient in nature.
\ Consequently,turbulence can not be tracked to lower Reynolds numbers, where
the dynamics may simplify. Before this happens, turbulence becomes short-lived
and laminarizes. In the last part of the thesis, we show that using numerical
simulations we can continue turbulent stripes in channel flow past the 'relaminarization
barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies
and the fluctuations are no longer stochastic and the stripe settles down to a
relative periodic orbit. This relative periodic orbit originates from the aforementioned
traveling wave solutions. Starting from the relative periodic orbit, a small increase
in speed i.e. Reynolds number gives rise to chaos and the attractor dimension
sharply increases in contrast to the classical transition scenario where the instabilities
affect the flow globally and give rise to much more gradual route to turbulence."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Chaitanya S
full_name: Paranjape, Chaitanya S
id: 3D85B7C4-F248-11E8-B48F-1D18A9856A87
last_name: Paranjape
citation:
ama: Paranjape CS. Onset of turbulence in plane Poiseuille flow. 2019. doi:10.15479/AT:ISTA:6957
apa: Paranjape, C. S. (2019). Onset of turbulence in plane Poiseuille flow.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:6957
chicago: Paranjape, Chaitanya S. “Onset of Turbulence in Plane Poiseuille Flow.”
Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:6957.
ieee: C. S. Paranjape, “Onset of turbulence in plane Poiseuille flow,” Institute
of Science and Technology Austria, 2019.
ista: Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow. Institute
of Science and Technology Austria.
mla: Paranjape, Chaitanya S. Onset of Turbulence in Plane Poiseuille Flow.
Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:6957.
short: C.S. Paranjape, Onset of Turbulence in Plane Poiseuille Flow, Institute of
Science and Technology Austria, 2019.
date_created: 2019-10-22T12:08:43Z
date_published: 2019-10-24T00:00:00Z
date_updated: 2023-09-07T12:53:25Z
day: '24'
ddc:
- '532'
degree_awarded: PhD
department:
- _id: BjHo
doi: 10.15479/AT:ISTA:6957
file:
- access_level: closed
checksum: 7ba298ba0ce7e1d11691af6b8eaf0a0a
content_type: application/zip
creator: cparanjape
date_created: 2019-10-23T09:54:43Z
date_updated: 2020-07-14T12:47:46Z
file_id: '6962'
file_name: Chaitanya_Paranjape_source_files_tex_figures.zip
file_size: 45828099
relation: source_file
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checksum: 642697618314e31ac31392da7909c2d9
content_type: application/pdf
creator: cparanjape
date_created: 2019-10-23T10:37:09Z
date_updated: 2020-07-14T12:47:46Z
file_id: '6963'
file_name: Chaitanya_Paranjape_Thesis.pdf
file_size: 19504197
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
keyword:
- Instabilities
- Turbulence
- Nonlinear dynamics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: '138'
publication_identifier:
eissn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: Björn
full_name: Hof, Björn
id: 3A374330-F248-11E8-B48F-1D18A9856A87
last_name: Hof
orcid: 0000-0003-2057-2754
title: Onset of turbulence in plane Poiseuille flow
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...