[{"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.","author":[{"id":"df755ffe-735a-11ee-bb55-dff29d61d338","orcid":"0000-0002-6229-0336","first_name":"Baoying","full_name":"Wang, Baoying","last_name":"Wang"},{"id":"ab77522d-073b-11ed-8aff-e71b39258362","orcid":"0000-0001-6572-0621","first_name":"Roger","full_name":"Ayats López, Roger","last_name":"Ayats López"},{"first_name":"K.","full_name":"Deguchi, K.","last_name":"Deguchi"},{"last_name":"Meseguer","full_name":"Meseguer, A.","first_name":"A."},{"last_name":"Mellibovsky","first_name":"F.","full_name":"Mellibovsky, F."}],"ddc":["530"],"article_number":"A36","external_id":{"isi":["001487354900001"]},"year":"2025","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Published Version","volume":1010,"date_published":"2025-05-14T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","title":"Feigenbaum universality in subcritical Taylor-Couette flow","has_accepted_license":"1","status":"public","publisher":"Cambridge University Press","publication":"Journal of Fluid Mechanics","OA_place":"publisher","publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"month":"05","intvolume":"      1010","date_created":"2025-05-25T22:16:48Z","publication_status":"published","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","department":[{"_id":"BjHo"}],"doi":"10.1017/jfm.2025.278","file":[{"creator":"dernst","date_created":"2025-05-28T08:32:33Z","file_size":3607069,"file_id":"19752","relation":"main_file","checksum":"77f39b762a0e59e88954afb93b23cc7a","success":1,"access_level":"open_access","date_updated":"2025-05-28T08:32:33Z","file_name":"2025_JourFluidMech_Wang.pdf","content_type":"application/pdf"}],"article_type":"original","day":"14","isi":1,"project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020"},{"grant_number":"ESP 1481224","name":"Pattern Formation Mechanisms in Planar Shear Flows","_id":"942a0200-16d5-11f0-9cad-f48ab22dfd1c"}],"OA_type":"hybrid","scopus_import":"1","ec_funded":1,"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."}],"language":[{"iso":"eng"}],"oa":1,"file_date_updated":"2025-05-28T08:32:33Z","citation":{"chicago":"Wang, Baoying, Roger Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky. “Feigenbaum Universality in Subcritical Taylor-Couette Flow.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/jfm.2025.278\">https://doi.org/10.1017/jfm.2025.278</a>.","short":"B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, F. Mellibovsky, Journal of Fluid Mechanics 1010 (2025).","mla":"Wang, Baoying, et al. “Feigenbaum Universality in Subcritical Taylor-Couette Flow.” <i>Journal of Fluid Mechanics</i>, vol. 1010, A36, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/jfm.2025.278\">10.1017/jfm.2025.278</a>.","ieee":"B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, and F. Mellibovsky, “Feigenbaum universality in subcritical Taylor-Couette flow,” <i>Journal of Fluid Mechanics</i>, vol. 1010. Cambridge University Press, 2025.","apa":"Wang, B., Ayats López, R., Deguchi, K., Meseguer, A., &#38; Mellibovsky, F. (2025). Feigenbaum universality in subcritical Taylor-Couette flow. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2025.278\">https://doi.org/10.1017/jfm.2025.278</a>","ama":"Wang B, Ayats López R, Deguchi K, Meseguer A, Mellibovsky F. Feigenbaum universality in subcritical Taylor-Couette flow. <i>Journal of Fluid Mechanics</i>. 2025;1010. doi:<a href=\"https://doi.org/10.1017/jfm.2025.278\">10.1017/jfm.2025.278</a>","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."},"quality_controlled":"1","date_updated":"2025-09-30T12:39:05Z","_id":"19730"},{"author":[{"orcid":"0000-0002-6229-0336","id":"df755ffe-735a-11ee-bb55-dff29d61d338","last_name":"Wang","full_name":"Wang, Baoying","first_name":"Baoying"},{"orcid":"0000-0001-6572-0621","id":"ab77522d-073b-11ed-8aff-e71b39258362","last_name":"Ayats López","full_name":"Ayats López, Roger","first_name":"Roger"},{"last_name":"Deguchi","first_name":"K.","full_name":"Deguchi, K."},{"full_name":"Meseguer, A.","first_name":"A.","last_name":"Meseguer"},{"first_name":"F.","full_name":"Mellibovsky, F.","last_name":"Mellibovsky"}],"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.","external_id":{"isi":["001486096600001"]},"ddc":["530"],"article_number":"R2","volume":1011,"date_published":"2025-05-13T00:00:00Z","oa_version":"Published Version","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","title":"Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow","article_processing_charge":"Yes (in subscription journal)","status":"public","has_accepted_license":"1","OA_place":"publisher","publication":"Journal of Fluid Mechanics","publisher":"Cambridge University Press","publication_identifier":{"eissn":["1469-7645"],"issn":["0022-1120"]},"intvolume":"      1011","month":"05","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","date_created":"2025-05-25T22:16:52Z","publication_status":"published","file":[{"file_id":"19754","relation":"main_file","date_created":"2025-05-28T09:00:52Z","file_size":998754,"creator":"dernst","content_type":"application/pdf","date_updated":"2025-05-28T09:00:52Z","file_name":"2025_JourFluidMech_Wang_Ayats.pdf","checksum":"899df5797844a9e811dffeebe8c05c8e","success":1,"access_level":"open_access"}],"department":[{"_id":"BjHo"}],"doi":"10.1017/jfm.2025.151","article_type":"original","project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"},{"grant_number":"ESP 1481224","name":"Pattern Formation Mechanisms in Planar Shear Flows","_id":"942a0200-16d5-11f0-9cad-f48ab22dfd1c"}],"isi":1,"day":"13","scopus_import":"1","OA_type":"hybrid","file_date_updated":"2025-05-28T09:00:52Z","oa":1,"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"quality_controlled":"1","date_updated":"2025-09-30T12:39:44Z","citation":{"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.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/jfm.2025.151\">https://doi.org/10.1017/jfm.2025.151</a>.","short":"B. Wang, R. Ayats López, K. Deguchi, A. Meseguer, F. Mellibovsky, Journal of Fluid Mechanics 1011 (2025).","mla":"Wang, Baoying, et al. “Mathematically Established Chaos and Forecast of Statistics with Recurrent Patterns in Taylor-Couette Flow.” <i>Journal of Fluid Mechanics</i>, vol. 1011, R2, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/jfm.2025.151\">10.1017/jfm.2025.151</a>.","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,” <i>Journal of Fluid Mechanics</i>, vol. 1011. Cambridge University Press, 2025.","apa":"Wang, B., Ayats López, R., Deguchi, K., Meseguer, A., &#38; Mellibovsky, F. (2025). Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2025.151\">https://doi.org/10.1017/jfm.2025.151</a>","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. <i>Journal of Fluid Mechanics</i>. 2025;1011. doi:<a href=\"https://doi.org/10.1017/jfm.2025.151\">10.1017/jfm.2025.151</a>","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."},"_id":"19732"}]