{"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.","status":"public","related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/turbulent-flow-simplified/"}]},"citation":{"ama":"Yalniz G, Hof B, Budanur NB. Coarse graining the state space of a turbulent flow using periodic orbits. <i>Physical Review Letters</i>. 2021;126(24). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">10.1103/PhysRevLett.126.244502</a>","chicago":"Yalniz, Gökhan, Björn Hof, and Nazmi B Budanur. “Coarse Graining the State Space of a Turbulent Flow Using Periodic Orbits.” <i>Physical Review Letters</i>. American Physical Society, 2021. <a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">https://doi.org/10.1103/PhysRevLett.126.244502</a>.","apa":"Yalniz, G., Hof, B., &#38; Budanur, N. B. (2021). Coarse graining the state space of a turbulent flow using periodic orbits. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">https://doi.org/10.1103/PhysRevLett.126.244502</a>","ieee":"G. Yalniz, B. Hof, and N. B. Budanur, “Coarse graining the state space of a turbulent flow using periodic orbits,” <i>Physical Review Letters</i>, vol. 126, no. 24. American Physical Society, 2021.","short":"G. Yalniz, B. Hof, N.B. Budanur, Physical Review Letters 126 (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.” <i>Physical Review Letters</i>, vol. 126, no. 24, 244502, American Physical Society, 2021, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.126.244502\">10.1103/PhysRevLett.126.244502</a>."},"publication":"Physical Review Letters","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/2007.02584","open_access":"1"}],"volume":126,"publication_status":"published","isi":1,"quality_controlled":"1","doi":"10.1103/PhysRevLett.126.244502","_id":"9558","year":"2021","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2023-08-08T14:08:36Z","author":[{"full_name":"Yalniz, Gökhan","last_name":"Yalniz","orcid":"0000-0002-8490-9312","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","first_name":"Gökhan"},{"full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","last_name":"Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn"},{"first_name":"Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0423-5010","last_name":"Budanur","full_name":"Budanur, Nazmi B"}],"external_id":{"arxiv":["2007.02584"],"isi":["000663310100008"]},"oa_version":"Preprint","date_published":"2021-06-18T00:00:00Z","abstract":[{"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","lang":"eng"}],"oa":1,"department":[{"_id":"GradSch"},{"_id":"BjHo"}],"publisher":"American Physical Society","article_type":"letter_note","article_number":"244502","type":"journal_article","intvolume":"       126","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960"}],"acknowledged_ssus":[{"_id":"ScienComp"}],"day":"18","issue":"24","title":"Coarse graining the state space of a turbulent flow using periodic orbits","article_processing_charge":"No","language":[{"iso":"eng"}],"date_created":"2021-06-16T15:45:36Z","publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]}}