--- _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 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 license: https://creativecommons.org/licenses/by/4.0/ 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: '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 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: '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 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 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: '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 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 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' ...