--- OA_place: publisher OA_type: hybrid _id: '19730' abstract: - lang: eng text: Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor–Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period-doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period-doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows. acknowledgement: This research is supported by the Australian Research Council Discovery Project DP230102188 and the Ministerio de Ciencia, Innovación y Universidades (Agencia Estatal de Investigación, project nos. PID 2020–114043 GB-I00 (MCIN/AEI/10.13039/501100011033) and PID 2023–150029NB-I00 (MCIN/AEI/10.13039/501100011033/FEDER, UE). B.W.’s and R.A.’s research has been funded by the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie Grant Agreement No. 101034413). R.A. has also been funded by the Austrian Science Fund (FWF) 10.55776/ESP1481224. article_number: A36 article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Baoying full_name: Wang, Baoying id: df755ffe-735a-11ee-bb55-dff29d61d338 last_name: Wang orcid: 0000-0002-6229-0336 - first_name: Roger full_name: Ayats López, Roger id: ab77522d-073b-11ed-8aff-e71b39258362 last_name: Ayats López orcid: 0000-0001-6572-0621 - first_name: K. full_name: Deguchi, K. last_name: Deguchi - first_name: A. full_name: Meseguer, A. last_name: Meseguer - first_name: F. full_name: Mellibovsky, F. last_name: Mellibovsky citation: ama: Wang B, Ayats López R, Deguchi K, Meseguer A, Mellibovsky F. Feigenbaum universality in subcritical Taylor-Couette flow. Journal of Fluid Mechanics. 2025;1010. doi:10.1017/jfm.2025.278 apa: Wang, B., Ayats López, R., Deguchi, K., Meseguer, A., & Mellibovsky, F. (2025). Feigenbaum universality in subcritical Taylor-Couette flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2025.278 chicago: Wang, Baoying, Roger Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky. “Feigenbaum Universality in Subcritical Taylor-Couette Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2025. https://doi.org/10.1017/jfm.2025.278. ieee: B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky, “Feigenbaum universality in subcritical Taylor-Couette flow,” Journal of Fluid Mechanics, vol. 1010. Cambridge University Press, 2025. ista: Wang B, Ayats López R, Deguchi K, Meseguer A, Mellibovsky F. 2025. Feigenbaum universality in subcritical Taylor-Couette flow. Journal of Fluid Mechanics. 1010, A36. mla: Wang, Baoying, et al. “Feigenbaum Universality in Subcritical Taylor-Couette Flow.” Journal of Fluid Mechanics, vol. 1010, A36, Cambridge University Press, 2025, doi:10.1017/jfm.2025.278. short: B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, F. Mellibovsky, Journal of Fluid Mechanics 1010 (2025). date_created: 2025-05-25T22:16:48Z date_published: 2025-05-14T00:00:00Z date_updated: 2025-09-30T12:39:05Z day: '14' ddc: - '530' department: - _id: BjHo doi: 10.1017/jfm.2025.278 ec_funded: 1 external_id: isi: - '001487354900001' file: - access_level: open_access checksum: 77f39b762a0e59e88954afb93b23cc7a content_type: application/pdf creator: dernst date_created: 2025-05-28T08:32:33Z date_updated: 2025-05-28T08:32:33Z file_id: '19752' file_name: 2025_JourFluidMech_Wang.pdf file_size: 3607069 relation: main_file success: 1 file_date_updated: 2025-05-28T08:32:33Z has_accepted_license: '1' intvolume: ' 1010' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' - _id: 942a0200-16d5-11f0-9cad-f48ab22dfd1c grant_number: ESP 1481224 name: Pattern Formation Mechanisms in Planar Shear 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: Feigenbaum universality in subcritical Taylor-Couette flow 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 1010 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19732' abstract: - lang: eng text: The transition to chaos in the subcritical regime of counter-rotating Taylor–Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics is found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier–Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs. acknowledgement: This research is supported by the Australian Research Council Discovery Project DP230102188 and the Ministerio de Ciencia, Innovación y Universidades (Agencia Estatal de Investigación, project nos PID 2020-114043 GB-I00 (MCIN/AEI/10.13039/501100011033) and PID 2023-150029NB-I00 (MCIN/AEI/10.13039/ 501100011033/FEDER, UE). B.W. and R.A.’s research has been funded by the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie grant agreement no. 101034413). R.A. has also been funded by the Austrian Science Fund (FWF) 10.55776/ESP1481224. article_number: R2 article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Baoying full_name: Wang, Baoying id: df755ffe-735a-11ee-bb55-dff29d61d338 last_name: Wang orcid: 0000-0002-6229-0336 - first_name: Roger full_name: Ayats López, Roger id: ab77522d-073b-11ed-8aff-e71b39258362 last_name: Ayats López orcid: 0000-0001-6572-0621 - first_name: K. full_name: Deguchi, K. last_name: Deguchi - first_name: A. full_name: Meseguer, A. last_name: Meseguer - first_name: F. full_name: Mellibovsky, F. last_name: Mellibovsky citation: ama: Wang B, Ayats López R, Deguchi K, Meseguer A, Mellibovsky F. Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow. Journal of Fluid Mechanics. 2025;1011. doi:10.1017/jfm.2025.151 apa: Wang, B., Ayats López, R., Deguchi, K., Meseguer, A., & Mellibovsky, F. (2025). Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2025.151 chicago: Wang, Baoying, Roger Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky. “Mathematically Established Chaos and Forecast of Statistics with Recurrent Patterns in Taylor-Couette Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2025. https://doi.org/10.1017/jfm.2025.151. ieee: B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky, “Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow,” Journal of Fluid Mechanics, vol. 1011. Cambridge University Press, 2025. ista: Wang B, Ayats López R, Deguchi K, Meseguer A, Mellibovsky F. 2025. Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow. Journal of Fluid Mechanics. 1011, R2. mla: Wang, Baoying, et al. “Mathematically Established Chaos and Forecast of Statistics with Recurrent Patterns in Taylor-Couette Flow.” Journal of Fluid Mechanics, vol. 1011, R2, Cambridge University Press, 2025, doi:10.1017/jfm.2025.151. short: B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, F. Mellibovsky, Journal of Fluid Mechanics 1011 (2025). date_created: 2025-05-25T22:16:52Z date_published: 2025-05-13T00:00:00Z date_updated: 2025-09-30T12:39:44Z day: '13' ddc: - '530' department: - _id: BjHo doi: 10.1017/jfm.2025.151 ec_funded: 1 external_id: isi: - '001486096600001' file: - access_level: open_access checksum: 899df5797844a9e811dffeebe8c05c8e content_type: application/pdf creator: dernst date_created: 2025-05-28T09:00:52Z date_updated: 2025-05-28T09:00:52Z file_id: '19754' file_name: 2025_JourFluidMech_Wang_Ayats.pdf file_size: 998754 relation: main_file success: 1 file_date_updated: 2025-05-28T09:00:52Z has_accepted_license: '1' intvolume: ' 1011' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' - _id: 942a0200-16d5-11f0-9cad-f48ab22dfd1c grant_number: ESP 1481224 name: Pattern Formation Mechanisms in Planar Shear 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: Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 1011 year: '2025' ...