---
_id: '14466'
abstract:
- lang: eng
text: The first long-lived turbulent structures observable in planar shear flows
take the form of localized stripes, inclined with respect to the mean flow direction.
The dynamics of these stripes is central to transition, and recent studies proposed
an analogy to directed percolation where the stripes’ proliferation is ultimately
responsible for the turbulence becoming sustained. In the present study we focus
on the internal stripe dynamics as well as on the eventual stripe expansion, and
we compare the underlying mechanisms in pressure- and shear-driven planar flows,
respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities
of the overall laminar–turbulence patterns, the stripe proliferation processes
in the two cases are fundamentally different. Starting from the growth and sustenance
of individual stripes, we find that in plane-Couette flow new streaks are created
stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation
is deterministic and occurs locally at the downstream tip. Because of the up/downstream
symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and
two strong laminar turbulent interfaces. These differences in symmetry as well
as in internal growth give rise to two fundamentally different stripe splitting
mechanisms. In plane-Poiseuille flow splitting is connected to the elongational
growth of the original stripe, and it results from a break-off/shedding of the
stripe's tail. In plane-Couette flow splitting follows from a broadening of the
original stripe and a division along the stripe into two slimmer stripes.
acknowledgement: E.M. acknowledges funding from the ISTplus fellowship programme.
G.Y. and B.H. acknowledge a grant from the Simons Foundation (662960, BH).
article_number: A21
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Elena
full_name: Marensi, Elena
id: 0BE7553A-1004-11EA-B805-18983DDC885E
last_name: Marensi
orcid: 0000-0001-7173-4923
- 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: Marensi E, Yalniz G, Hof B. Dynamics and proliferation of turbulent stripes
in plane-Poiseuille and plane-Couette flows. Journal of Fluid Mechanics.
2023;974. doi:10.1017/jfm.2023.780
apa: Marensi, E., Yalniz, G., & Hof, B. (2023). Dynamics and proliferation of
turbulent stripes in plane-Poiseuille and plane-Couette flows. Journal of Fluid
Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2023.780
chicago: Marensi, Elena, Gökhan Yalniz, and Björn Hof. “Dynamics and Proliferation
of Turbulent Stripes in Plane-Poiseuille and Plane-Couette Flows.” Journal
of Fluid Mechanics. Cambridge University Press, 2023. https://doi.org/10.1017/jfm.2023.780.
ieee: E. Marensi, G. Yalniz, and B. Hof, “Dynamics and proliferation of turbulent
stripes in plane-Poiseuille and plane-Couette flows,” Journal of Fluid Mechanics,
vol. 974. Cambridge University Press, 2023.
ista: Marensi E, Yalniz G, Hof B. 2023. Dynamics and proliferation of turbulent
stripes in plane-Poiseuille and plane-Couette flows. Journal of Fluid Mechanics.
974, A21.
mla: Marensi, Elena, et al. “Dynamics and Proliferation of Turbulent Stripes in
Plane-Poiseuille and Plane-Couette Flows.” Journal of Fluid Mechanics,
vol. 974, A21, Cambridge University Press, 2023, doi:10.1017/jfm.2023.780.
short: E. Marensi, G. Yalniz, B. Hof, Journal of Fluid Mechanics 974 (2023).
date_created: 2023-10-30T09:32:28Z
date_published: 2023-11-10T00:00:00Z
date_updated: 2024-02-15T09:06:23Z
day: '10'
ddc:
- '530'
department:
- _id: GradSch
- _id: BjHo
doi: 10.1017/jfm.2023.780
external_id:
arxiv:
- '2212.12406'
isi:
- '001088363700001'
file:
- access_level: open_access
checksum: 17c64c1fb0d5f73252364bf98b0b9e1a
content_type: application/pdf
creator: dernst
date_created: 2024-02-15T09:05:21Z
date_updated: 2024-02-15T09:05:21Z
file_id: '14996'
file_name: 2023_JourFluidMechanics_Marensi.pdf
file_size: 2804641
relation: main_file
success: 1
file_date_updated: 2024-02-15T09:05:21Z
has_accepted_license: '1'
intvolume: ' 974'
isi: 1
keyword:
- turbulence
- transition to turbulence
- patterns
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
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: Journal of Fluid Mechanics
publication_identifier:
eissn:
- 1469-7645
issn:
- 0022-1120
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette
flows
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: 974
year: '2023'
...
---
_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: '12105'
abstract:
- lang: eng
text: Data-driven dimensionality reduction methods such as proper orthogonal decomposition
and dynamic mode decomposition have proven to be useful for exploring complex
phenomena within fluid dynamics and beyond. A well-known challenge for these techniques
is posed by the continuous symmetries, e.g. translations and rotations, of the
system under consideration, as drifts in the data dominate the modal expansions
without providing an insight into the dynamics of the problem. In the present
study, we address this issue for fluid flows in rectangular channels by formulating
a continuous symmetry reduction method that eliminates the translations in the
streamwise and spanwise directions simultaneously. We demonstrate our method by
computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows
of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille
flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity
of the invariant solutions with translation symmetries, i.e. travelling waves
and relative periodic orbits, whereas in the latter, our calculations reveal episodes
of turbulent time evolution that can be approximated by a low-dimensional linear
expansion.
acknowledgement: "E.M. acknowledges funding from the ISTplus fellowship programme.
G.Y. and B.H. acknowledge\r\na grant from the Simons Foundation (662960, BH)."
article_number: A10
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Elena
full_name: Marensi, Elena
id: 0BE7553A-1004-11EA-B805-18983DDC885E
last_name: Marensi
- 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
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
citation:
ama: Marensi E, Yalniz G, Hof B, Budanur NB. Symmetry-reduced dynamic mode decomposition
of near-wall turbulence. Journal of Fluid Mechanics. 2023;954. doi:10.1017/jfm.2022.1001
apa: Marensi, E., Yalniz, G., Hof, B., & Budanur, N. B. (2023). Symmetry-reduced
dynamic mode decomposition of near-wall turbulence. Journal of Fluid Mechanics.
Cambridge University Press. https://doi.org/10.1017/jfm.2022.1001
chicago: Marensi, Elena, Gökhan Yalniz, Björn Hof, and Nazmi B Budanur. “Symmetry-Reduced
Dynamic Mode Decomposition of near-Wall Turbulence.” Journal of Fluid Mechanics.
Cambridge University Press, 2023. https://doi.org/10.1017/jfm.2022.1001.
ieee: E. Marensi, G. Yalniz, B. Hof, and N. B. Budanur, “Symmetry-reduced dynamic
mode decomposition of near-wall turbulence,” Journal of Fluid Mechanics,
vol. 954. Cambridge University Press, 2023.
ista: Marensi E, Yalniz G, Hof B, Budanur NB. 2023. Symmetry-reduced dynamic mode
decomposition of near-wall turbulence. Journal of Fluid Mechanics. 954, A10.
mla: Marensi, Elena, et al. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall
Turbulence.” Journal of Fluid Mechanics, vol. 954, A10, Cambridge University
Press, 2023, doi:10.1017/jfm.2022.1001.
short: E. Marensi, G. Yalniz, B. Hof, N.B. Budanur, Journal of Fluid Mechanics 954
(2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-10T00:00:00Z
date_updated: 2023-08-01T12:53:23Z
day: '10'
ddc:
- '530'
department:
- _id: BjHo
doi: 10.1017/jfm.2022.1001
external_id:
arxiv:
- '2101.07516'
isi:
- '000903336600001'
file:
- access_level: open_access
checksum: 9224f987caefe5dd85a70814d3cce65c
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T12:34:54Z
date_updated: 2023-02-02T12:34:54Z
file_id: '12489'
file_name: 2023_JourFluidMechanics_Marensi.pdf
file_size: 1931647
relation: main_file
success: 1
file_date_updated: 2023-02-02T12:34:54Z
has_accepted_license: '1'
intvolume: ' 954'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
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: 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: Symmetry-reduced dynamic mode decomposition of near-wall 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 954
year: '2023'
...
---
_id: '9558'
abstract:
- lang: eng
text: "We show that turbulent dynamics that arise in simulations of the three-dimensional
Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing
can be described as transient visits to the neighborhoods of unstable time-periodic
solutions. Based on this description, we reduce the original system with more
than 10^5 degrees of freedom to a 17-node Markov chain where each node corresponds
to the neighborhood of a periodic orbit. The model accurately reproduces long-term
averages of the system's observables as weighted sums over the periodic orbits.\r\n"
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "We thank the referees for improving this Letter with their comments.
We acknowledge stimulating discussions with\r\nH. Edelsbrunner. This work was supported
by Grant No. 662960 from the Simons Foundation (B. H.). The numerical calculations
were performed at TUBITAK ULAKBIM High Performance and Grid Computing Center (TRUBA
resources) and IST Austria High Performance Computing cluster."
article_number: '244502'
article_processing_charge: No
article_type: letter_note
arxiv: 1
author:
- 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
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
citation:
ama: Yalniz G, Hof B, Budanur NB. Coarse graining the state space of a turbulent
flow using periodic orbits. Physical Review Letters. 2021;126(24). doi:10.1103/PhysRevLett.126.244502
apa: Yalniz, G., Hof, B., & Budanur, N. B. (2021). Coarse graining the state
space of a turbulent flow using periodic orbits. Physical Review Letters.
American Physical Society. https://doi.org/10.1103/PhysRevLett.126.244502
chicago: Yalniz, Gökhan, Björn Hof, and Nazmi B Budanur. “Coarse Graining the State
Space of a Turbulent Flow Using Periodic Orbits.” Physical Review Letters.
American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.244502.
ieee: G. Yalniz, B. Hof, and N. B. Budanur, “Coarse graining the state space of
a turbulent flow using periodic orbits,” Physical Review Letters, vol.
126, no. 24. American Physical Society, 2021.
ista: Yalniz G, Hof B, Budanur NB. 2021. Coarse graining the state space of a turbulent
flow using periodic orbits. Physical Review Letters. 126(24), 244502.
mla: Yalniz, Gökhan, et al. “Coarse Graining the State Space of a Turbulent Flow
Using Periodic Orbits.” Physical Review Letters, vol. 126, no. 24, 244502,
American Physical Society, 2021, doi:10.1103/PhysRevLett.126.244502.
short: G. Yalniz, B. Hof, N.B. Budanur, Physical Review Letters 126 (2021).
date_created: 2021-06-16T15:45:36Z
date_published: 2021-06-18T00:00:00Z
date_updated: 2023-08-08T14:08:36Z
day: '18'
department:
- _id: GradSch
- _id: BjHo
doi: 10.1103/PhysRevLett.126.244502
external_id:
arxiv:
- '2007.02584'
isi:
- '000663310100008'
intvolume: ' 126'
isi: 1
issue: '24'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2007.02584
month: '06'
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'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/turbulent-flow-simplified/
status: public
title: Coarse graining the state space of a turbulent flow using periodic orbits
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 126
year: '2021'
...
---
_id: '7563'
abstract:
- lang: eng
text: "We introduce “state space persistence analysis” for deducing the symbolic
dynamics of time series data obtained from high-dimensional chaotic attractors.
To this end, we adapt a topological data analysis technique known as persistent
homology for the characterization of state space projections of chaotic trajectories
and periodic orbits. By comparing the shapes along a chaotic trajectory to those
of the periodic orbits, state space persistence analysis quantifies the shape
similarity of chaotic trajectory segments and periodic orbits. We demonstrate
the method by applying it to the three-dimensional Rössler system and a 30-dimensional
discretization of the Kuramoto–Sivashinsky partial differential equation in (1+1)
dimensions.\r\nOne way of studying chaotic attractors systematically is through
their symbolic dynamics, in which one partitions the state space into qualitatively
different regions and assigns a symbol to each such region.1–3 This yields a “coarse-grained”
state space of the system, which can then be reduced to a Markov chain encoding
all possible transitions between the states of the system. While it is possible
to obtain the symbolic dynamics of low-dimensional chaotic systems with standard
tools such as Poincaré maps, when applied to high-dimensional systems such as
turbulent flows, these tools alone are not sufficient to determine symbolic dynamics.4,5
In this paper, we develop “state space persistence analysis” and demonstrate that
it can be utilized to infer the symbolic dynamics in very high-dimensional settings."
article_number: '033109'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gökhan
full_name: Yalniz, Gökhan
id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
last_name: Yalniz
orcid: 0000-0002-8490-9312
- first_name: Nazmi B
full_name: Budanur, Nazmi B
id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
last_name: Budanur
orcid: 0000-0003-0423-5010
citation:
ama: Yalniz G, Budanur NB. Inferring symbolic dynamics of chaotic flows from persistence.
Chaos. 2020;30(3). doi:10.1063/1.5122969
apa: Yalniz, G., & Budanur, N. B. (2020). Inferring symbolic dynamics of chaotic
flows from persistence. Chaos. AIP Publishing. https://doi.org/10.1063/1.5122969
chicago: Yalniz, Gökhan, and Nazmi B Budanur. “Inferring Symbolic Dynamics of Chaotic
Flows from Persistence.” Chaos. AIP Publishing, 2020. https://doi.org/10.1063/1.5122969.
ieee: G. Yalniz and N. B. Budanur, “Inferring symbolic dynamics of chaotic flows
from persistence,” Chaos, vol. 30, no. 3. AIP Publishing, 2020.
ista: Yalniz G, Budanur NB. 2020. Inferring symbolic dynamics of chaotic flows from
persistence. Chaos. 30(3), 033109.
mla: Yalniz, Gökhan, and Nazmi B. Budanur. “Inferring Symbolic Dynamics of Chaotic
Flows from Persistence.” Chaos, vol. 30, no. 3, 033109, AIP Publishing,
2020, doi:10.1063/1.5122969.
short: G. Yalniz, N.B. Budanur, Chaos 30 (2020).
date_created: 2020-03-04T08:06:25Z
date_published: 2020-03-03T00:00:00Z
date_updated: 2023-08-18T06:47:16Z
day: '03'
department:
- _id: BjHo
doi: 10.1063/1.5122969
external_id:
arxiv:
- '1910.04584'
isi:
- '000519254800002'
intvolume: ' 30'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1063/1.5122969
month: '03'
oa: 1
oa_version: Published Version
publication: Chaos
publication_identifier:
eissn:
- 1089-7682
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inferring symbolic dynamics of chaotic flows from persistence
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 30
year: '2020'
...