[{"abstract":[{"text":"Flows through pipes and channels are, in practice, almost always turbulent, and the multiscale eddying motion is responsible for a major part of the encountered friction losses and pumping costs1. Conversely, for pulsatile flows, in particular for aortic blood flow, turbulence levels remain low despite relatively large peak velocities. For aortic blood flow, high turbulence levels are intolerable as they would damage the shear-sensitive endothelial cell layer2,3,4,5. Here we show that turbulence in ordinary pipe flow is diminished if the flow is driven in a pulsatile mode that incorporates all the key features of the cardiac waveform. At Reynolds numbers comparable to those of aortic blood flow, turbulence is largely inhibited, whereas at much higher speeds, the turbulent drag is reduced by more than 25%. This specific operation mode is more efficient when compared with steady driving, which is the present situation for virtually all fluid transport processes ranging from heating circuits to water, gas and oil pipelines.","lang":"eng"}],"doi":"10.1038/s41586-023-06399-5","day":"07","external_id":{"pmid":["37673988"]},"date_updated":"2023-09-20T12:10:22Z","citation":{"short":"D. Scarselli, J.M. Lopez Alonso, A. Varshney, B. Hof, Nature 621 (2023) 71–74.","mla":"Scarselli, Davide, et al. “Turbulence Suppression by Cardiac-Cycle-Inspired Driving of Pipe Flow.” <i>Nature</i>, vol. 621, no. 7977, Springer Nature, 2023, pp. 71–74, doi:<a href=\"https://doi.org/10.1038/s41586-023-06399-5\">10.1038/s41586-023-06399-5</a>.","ista":"Scarselli D, Lopez Alonso JM, Varshney A, Hof B. 2023. Turbulence suppression by cardiac-cycle-inspired driving of pipe flow. Nature. 621(7977), 71–74.","apa":"Scarselli, D., Lopez Alonso, J. M., Varshney, A., &#38; Hof, B. (2023). Turbulence suppression by cardiac-cycle-inspired driving of pipe flow. <i>Nature</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41586-023-06399-5\">https://doi.org/10.1038/s41586-023-06399-5</a>","ama":"Scarselli D, Lopez Alonso JM, Varshney A, Hof B. Turbulence suppression by cardiac-cycle-inspired driving of pipe flow. <i>Nature</i>. 2023;621(7977):71-74. doi:<a href=\"https://doi.org/10.1038/s41586-023-06399-5\">10.1038/s41586-023-06399-5</a>","chicago":"Scarselli, Davide, Jose M Lopez Alonso, Atul Varshney, and Björn Hof. “Turbulence Suppression by Cardiac-Cycle-Inspired Driving of Pipe Flow.” <i>Nature</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1038/s41586-023-06399-5\">https://doi.org/10.1038/s41586-023-06399-5</a>.","ieee":"D. Scarselli, J. M. Lopez Alonso, A. Varshney, and B. Hof, “Turbulence suppression by cardiac-cycle-inspired driving of pipe flow,” <i>Nature</i>, vol. 621, no. 7977. Springer Nature, pp. 71–74, 2023."},"year":"2023","volume":621,"acknowledgement":"We acknowledge the assistance of the Miba machine shop and the team of the ISTA-HPC cluster. We thank M. Quadrio for the discussions. The work was supported by the Simons Foundation (grant no. 662960) and by the Austrian Science Fund (grant no. I4188-N30), within Deutsche Forschungsgemeinschaft research unit FOR 2688.","title":"Turbulence suppression by cardiac-cycle-inspired driving of pipe flow","intvolume":"       621","publication_status":"published","department":[{"_id":"BjHo"}],"date_created":"2023-09-17T22:01:09Z","article_processing_charge":"No","author":[{"last_name":"Scarselli","first_name":"Davide","full_name":"Scarselli, Davide","orcid":"0000-0001-5227-4271","id":"40315C30-F248-11E8-B48F-1D18A9856A87"},{"id":"40770848-F248-11E8-B48F-1D18A9856A87","last_name":"Lopez Alonso","first_name":"Jose M","full_name":"Lopez Alonso, Jose M","orcid":"0000-0002-0384-2022"},{"id":"2A2006B2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-3072-5999","full_name":"Varshney, Atul","first_name":"Atul","last_name":"Varshney"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","last_name":"Hof","first_name":"Björn"}],"issue":"7977","pmid":1,"_id":"14341","scopus_import":"1","article_type":"original","publisher":"Springer Nature","page":"71-74","quality_controlled":"1","publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"date_published":"2023-09-07T00:00:00Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"link":[{"description":"News on ISTA website","relation":"press_release","url":"https://www.ista.ac.at/en/news/pumping-like-the-heart/"}]},"status":"public","month":"09","oa_version":"None","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"ScienComp"}],"project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"},{"call_identifier":"FWF","_id":"238B8092-32DE-11EA-91FC-C7463DDC885E","grant_number":"I04188","name":"Instabilities in pulsating pipe flow of Newtonian and complex fluids"}],"publication":"Nature","language":[{"iso":"eng"}]},{"acknowledgement":"E.M. acknowledges funding from the ISTplus fellowship programme. G.Y. and B.H. acknowledge a grant from the Simons Foundation (662960, BH).","volume":974,"ddc":["530"],"date_updated":"2024-02-15T09:06:23Z","citation":{"ieee":"E. Marensi, G. Yalniz, and B. Hof, “Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows,” <i>Journal of Fluid Mechanics</i>, vol. 974. Cambridge University Press, 2023.","chicago":"Marensi, Elena, Gökhan Yalniz, and Björn Hof. “Dynamics and Proliferation of Turbulent Stripes in Plane-Poiseuille and Plane-Couette Flows.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/jfm.2023.780\">https://doi.org/10.1017/jfm.2023.780</a>.","ama":"Marensi E, Yalniz G, Hof B. Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows. <i>Journal of Fluid Mechanics</i>. 2023;974. doi:<a href=\"https://doi.org/10.1017/jfm.2023.780\">10.1017/jfm.2023.780</a>","apa":"Marensi, E., Yalniz, G., &#38; Hof, B. (2023). Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2023.780\">https://doi.org/10.1017/jfm.2023.780</a>","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.” <i>Journal of Fluid Mechanics</i>, vol. 974, A21, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/jfm.2023.780\">10.1017/jfm.2023.780</a>.","short":"E. Marensi, G. Yalniz, B. Hof, Journal of Fluid Mechanics 974 (2023)."},"year":"2023","isi":1,"external_id":{"arxiv":["2212.12406"],"isi":["001088363700001"]},"doi":"10.1017/jfm.2023.780","arxiv":1,"day":"10","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."}],"quality_controlled":"1","file_date_updated":"2024-02-15T09:05:21Z","publisher":"Cambridge University Press","article_type":"original","_id":"14466","author":[{"id":"0BE7553A-1004-11EA-B805-18983DDC885E","full_name":"Marensi, Elena","orcid":"0000-0001-7173-4923","last_name":"Marensi","first_name":"Elena"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","last_name":"Yalniz","first_name":"Gökhan","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","last_name":"Hof","first_name":"Björn","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754"}],"publication_status":"published","article_processing_charge":"Yes (via OA deal)","date_created":"2023-10-30T09:32:28Z","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"title":"Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows","intvolume":"       974","file":[{"creator":"dernst","file_id":"14996","relation":"main_file","access_level":"open_access","success":1,"content_type":"application/pdf","file_name":"2023_JourFluidMechanics_Marensi.pdf","date_updated":"2024-02-15T09:05:21Z","file_size":2804641,"checksum":"17c64c1fb0d5f73252364bf98b0b9e1a","date_created":"2024-02-15T09:05:21Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2023-11-10T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0022-1120"],"eissn":["1469-7645"]},"oa":1,"language":[{"iso":"eng"}],"keyword":["turbulence","transition to turbulence","patterns"],"publication":"Journal of Fluid Mechanics","has_accepted_license":"1","oa_version":"Published Version","project":[{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","grant_number":"662960"}],"month":"11","article_number":"A21"},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05098"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2023-07-21T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"oa":1,"language":[{"iso":"eng"}],"keyword":["General Physics and Astronomy"],"publication":"Physical Review Letters","oa_version":"Preprint","project":[{"grant_number":"662960","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"month":"07","article_number":"034002","volume":131,"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.).","date_updated":"2023-12-13T11:40:19Z","year":"2023","citation":{"chicago":"Paranjape, Chaitanya S, Gökhan Yalniz, Yohann Duguet, Nazmi B Budanur, and Björn Hof. “Direct Path from Turbulence to Time-Periodic Solutions.” <i>Physical Review Letters</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/physrevlett.131.034002\">https://doi.org/10.1103/physrevlett.131.034002</a>.","ieee":"C. S. Paranjape, G. Yalniz, Y. Duguet, N. B. Budanur, and B. Hof, “Direct path from turbulence to time-periodic solutions,” <i>Physical Review Letters</i>, vol. 131, no. 3. American Physical Society, 2023.","ama":"Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. Direct path from turbulence to time-periodic solutions. <i>Physical Review Letters</i>. 2023;131(3). doi:<a href=\"https://doi.org/10.1103/physrevlett.131.034002\">10.1103/physrevlett.131.034002</a>","apa":"Paranjape, C. S., Yalniz, G., Duguet, Y., Budanur, N. B., &#38; Hof, B. (2023). Direct path from turbulence to time-periodic solutions. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.131.034002\">https://doi.org/10.1103/physrevlett.131.034002</a>","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.","short":"C.S. Paranjape, G. Yalniz, Y. Duguet, N.B. Budanur, B. Hof, Physical Review Letters 131 (2023).","mla":"Paranjape, Chaitanya S., et al. “Direct Path from Turbulence to Time-Periodic Solutions.” <i>Physical Review Letters</i>, vol. 131, no. 3, 034002, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/physrevlett.131.034002\">10.1103/physrevlett.131.034002</a>."},"isi":1,"external_id":{"arxiv":["2306.05098"],"isi":["001052929900004"]},"arxiv":1,"doi":"10.1103/physrevlett.131.034002","day":"21","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."}],"quality_controlled":"1","publisher":"American Physical Society","article_type":"original","_id":"13274","author":[{"full_name":"Paranjape, Chaitanya S","last_name":"Paranjape","first_name":"Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","first_name":"Gökhan","last_name":"Yalniz","orcid":"0000-0002-8490-9312","full_name":"Yalniz, Gökhan"},{"full_name":"Duguet, Yohann","first_name":"Yohann","last_name":"Duguet"},{"id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B","first_name":"Nazmi B","last_name":"Budanur"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","last_name":"Hof","first_name":"Björn","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754"}],"issue":"3","publication_status":"published","article_processing_charge":"No","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"date_created":"2023-07-24T09:43:59Z","title":"Direct path from turbulence to time-periodic solutions","intvolume":"       131"},{"ddc":["530"],"volume":954,"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).","abstract":[{"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.","lang":"eng"}],"day":"10","arxiv":1,"doi":"10.1017/jfm.2022.1001","external_id":{"arxiv":["2101.07516"],"isi":["000903336600001"]},"isi":1,"citation":{"chicago":"Marensi, Elena, Gökhan Yalniz, Björn Hof, and Nazmi B Budanur. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/jfm.2022.1001\">https://doi.org/10.1017/jfm.2022.1001</a>.","ieee":"E. Marensi, G. Yalniz, B. Hof, and N. B. Budanur, “Symmetry-reduced dynamic mode decomposition of near-wall turbulence,” <i>Journal of Fluid Mechanics</i>, vol. 954. Cambridge University Press, 2023.","apa":"Marensi, E., Yalniz, G., Hof, B., &#38; Budanur, N. B. (2023). Symmetry-reduced dynamic mode decomposition of near-wall turbulence. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2022.1001\">https://doi.org/10.1017/jfm.2022.1001</a>","ama":"Marensi E, Yalniz G, Hof B, Budanur NB. Symmetry-reduced dynamic mode decomposition of near-wall turbulence. <i>Journal of Fluid Mechanics</i>. 2023;954. doi:<a href=\"https://doi.org/10.1017/jfm.2022.1001\">10.1017/jfm.2022.1001</a>","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.","short":"E. Marensi, G. Yalniz, B. Hof, N.B. Budanur, Journal of Fluid Mechanics 954 (2023).","mla":"Marensi, Elena, et al. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” <i>Journal of Fluid Mechanics</i>, vol. 954, A10, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/jfm.2022.1001\">10.1017/jfm.2022.1001</a>."},"year":"2023","date_updated":"2023-08-01T12:53:23Z","article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2023-02-02T12:34:54Z","quality_controlled":"1","intvolume":"       954","title":"Symmetry-reduced dynamic mode decomposition of near-wall turbulence","date_created":"2023-01-08T23:00:53Z","department":[{"_id":"BjHo"}],"article_processing_charge":"Yes (via OA deal)","publication_status":"published","author":[{"full_name":"Marensi, Elena","first_name":"Elena","last_name":"Marensi","id":"0BE7553A-1004-11EA-B805-18983DDC885E"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312","last_name":"Yalniz","first_name":"Gökhan"},{"last_name":"Hof","first_name":"Björn","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87"},{"id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","first_name":"Nazmi B","last_name":"Budanur","orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B"}],"scopus_import":"1","_id":"12105","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"relation":"main_file","success":1,"access_level":"open_access","creator":"dernst","file_id":"12489","file_size":1931647,"checksum":"9224f987caefe5dd85a70814d3cce65c","date_created":"2023-02-02T12:34:54Z","file_name":"2023_JourFluidMechanics_Marensi.pdf","content_type":"application/pdf","date_updated":"2023-02-02T12:34:54Z"}],"oa":1,"publication_identifier":{"eissn":["1469-7645"],"issn":["0022-1120"]},"type":"journal_article","date_published":"2023-01-10T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"article_number":"A10","month":"01","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"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Journal of Fluid Mechanics"},{"publisher":"Annual Reviews","article_type":"original","page":"575-602","quality_controlled":"1","file_date_updated":"2023-02-27T09:35:52Z","publication_status":"published","department":[{"_id":"BjHo"}],"article_processing_charge":"No","date_created":"2023-02-26T23:01:01Z","title":"Transition to turbulence in pipe flow","intvolume":"        55","_id":"12682","scopus_import":"1","author":[{"last_name":"Avila","first_name":"Marc","full_name":"Avila, Marc"},{"full_name":"Barkley, Dwight","first_name":"Dwight","last_name":"Barkley"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","last_name":"Hof","first_name":"Björn","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754"}],"volume":55,"acknowledgement":"The authors are very grateful to Laurette Tuckerman for her helpful comments. This work was supported by grants from the Simons Foundation (grant numbers 662985, D.B., and 662960, B.H.) and the Priority Programme “SPP 1881: Turbulent Superstructures” of the Deutsche Forschungsgemeinschaft (grant number AV120/3-2 to M.A.).","ddc":["530"],"doi":"10.1146/annurev-fluid-120720-025957","day":"19","abstract":[{"text":"Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has served as a primary prototype for investigating the transition to turbulence in wall-bounded flows. Despite the apparent simplicity of this flow, various facets of this problem have occupied researchers for more than a century. Here we review insights from three distinct perspectives: (a) stability and susceptibility of laminar flow, (b) phase transition and spatiotemporal dynamics, and (c) dynamical systems analysis of the Navier—Stokes equations. We show how these perspectives have led to a profound understanding of the onset of turbulence in pipe flow. Outstanding open points, applications to flows of complex fluids, and similarities with other wall-bounded flows are discussed.","lang":"eng"}],"date_updated":"2023-08-01T13:20:30Z","year":"2023","citation":{"ieee":"M. Avila, D. Barkley, and B. Hof, “Transition to turbulence in pipe flow,” <i>Annual Review of Fluid Mechanics</i>, vol. 55. Annual Reviews, pp. 575–602, 2023.","chicago":"Avila, Marc, Dwight Barkley, and Björn Hof. “Transition to Turbulence in Pipe Flow.” <i>Annual Review of Fluid Mechanics</i>. Annual Reviews, 2023. <a href=\"https://doi.org/10.1146/annurev-fluid-120720-025957\">https://doi.org/10.1146/annurev-fluid-120720-025957</a>.","ama":"Avila M, Barkley D, Hof B. Transition to turbulence in pipe flow. <i>Annual Review of Fluid Mechanics</i>. 2023;55:575-602. doi:<a href=\"https://doi.org/10.1146/annurev-fluid-120720-025957\">10.1146/annurev-fluid-120720-025957</a>","apa":"Avila, M., Barkley, D., &#38; Hof, B. (2023). Transition to turbulence in pipe flow. <i>Annual Review of Fluid Mechanics</i>. Annual Reviews. <a href=\"https://doi.org/10.1146/annurev-fluid-120720-025957\">https://doi.org/10.1146/annurev-fluid-120720-025957</a>","ista":"Avila M, Barkley D, Hof B. 2023. Transition to turbulence in pipe flow. Annual Review of Fluid Mechanics. 55, 575–602.","mla":"Avila, Marc, et al. “Transition to Turbulence in Pipe Flow.” <i>Annual Review of Fluid Mechanics</i>, vol. 55, Annual Reviews, 2023, pp. 575–602, doi:<a href=\"https://doi.org/10.1146/annurev-fluid-120720-025957\">10.1146/annurev-fluid-120720-025957</a>.","short":"M. Avila, D. Barkley, B. Hof, Annual Review of Fluid Mechanics 55 (2023) 575–602."},"isi":1,"external_id":{"isi":["000915418100023"]},"language":[{"iso":"eng"}],"oa_version":"Published Version","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"month":"01","publication":"Annual Review of Fluid Mechanics","has_accepted_license":"1","file":[{"file_id":"12691","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access","date_updated":"2023-02-27T09:35:52Z","file_name":"2023_AnnReviewFluidMech_Avila.pdf","content_type":"application/pdf","date_created":"2023-02-27T09:35:52Z","file_size":4769537,"checksum":"f99ef30f76cabc9e5e1946b380c16db4"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0066-4189"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2023-01-19T00:00:00Z","type":"journal_article"},{"volume":128,"acknowledgement":"We thank T.Menner, T.Asenov, P. Maier and the Miba machine shop of IST Austria for their valuable support in all technical aspects. We thank Marc Avila for comments on the manuscript. This work was supported by a grant from the Simons Foundation (662960, B.H.). We acknowledge the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. K.A.\r\nacknowledges funding from the Central Research Development Fund of the University of Bremen, grant number ZF04B /2019/FB04 Avila Kerstin (”Independent Project for Postdocs”). L.K. was supported by the European Union’s Horizon 2020 Research and innovation programme under the Marie Sklodowska-Curie grant agreement  No. 754411.\r\n","day":"05","arxiv":1,"doi":"10.1103/PhysRevLett.128.014502","abstract":[{"text":"Directed percolation (DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however, experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows’ characteristic timescales. An exception is cylindrical Couette flow where the limit is not temporal, but rather the realizable system size. We present experiments in a Couette setup of unprecedented azimuthal and axial aspect ratios. Approaching the critical point to within less than 0.1% we determine five critical exponents, all of which are in excellent agreement with the 2+1D DP universality class. The complex dynamics encountered at \r\nthe onset of turbulence can hence be fully rationalized within the framework of statistical mechanics.","lang":"eng"}],"citation":{"ista":"Klotz L, Lemoult GM, Avila K, Hof B. 2022. Phase transition to turbulence in spatially extended shear flows. Physical Review Letters. 128(1), 014502.","short":"L. Klotz, G.M. Lemoult, K. Avila, B. Hof, Physical Review Letters 128 (2022).","mla":"Klotz, Lukasz, et al. “Phase Transition to Turbulence in Spatially Extended Shear Flows.” <i>Physical Review Letters</i>, vol. 128, no. 1, 014502, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.128.014502\">10.1103/PhysRevLett.128.014502</a>.","ieee":"L. Klotz, G. M. Lemoult, K. Avila, and B. Hof, “Phase transition to turbulence in spatially extended shear flows,” <i>Physical Review Letters</i>, vol. 128, no. 1. American Physical Society, 2022.","chicago":"Klotz, Lukasz, Grégoire M Lemoult, Kerstin Avila, and Björn Hof. “Phase Transition to Turbulence in Spatially Extended Shear Flows.” <i>Physical Review Letters</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/PhysRevLett.128.014502\">https://doi.org/10.1103/PhysRevLett.128.014502</a>.","apa":"Klotz, L., Lemoult, G. M., Avila, K., &#38; Hof, B. (2022). Phase transition to turbulence in spatially extended shear flows. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.128.014502\">https://doi.org/10.1103/PhysRevLett.128.014502</a>","ama":"Klotz L, Lemoult GM, Avila K, Hof B. Phase transition to turbulence in spatially extended shear flows. <i>Physical Review Letters</i>. 2022;128(1). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.128.014502\">10.1103/PhysRevLett.128.014502</a>"},"year":"2022","date_updated":"2023-08-02T13:59:19Z","external_id":{"isi":["000748271700010"],"pmid":["35061458"],"arxiv":["2111.14894"]},"isi":1,"publisher":"American Physical Society","article_type":"original","ec_funded":1,"quality_controlled":"1","date_created":"2022-01-23T23:01:28Z","department":[{"_id":"BjHo"}],"article_processing_charge":"No","publication_status":"published","intvolume":"       128","title":"Phase transition to turbulence in spatially extended shear flows","scopus_import":"1","_id":"10654","pmid":1,"issue":"1","author":[{"id":"2C9AF1C2-F248-11E8-B48F-1D18A9856A87","last_name":"Klotz","first_name":"Lukasz","full_name":"Klotz, Lukasz","orcid":"0000-0003-1740-7635"},{"id":"4787FE80-F248-11E8-B48F-1D18A9856A87","last_name":"Lemoult","first_name":"Grégoire M","full_name":"Lemoult, Grégoire M"},{"full_name":"Avila, Kerstin","first_name":"Kerstin","last_name":"Avila"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","last_name":"Hof","orcid":"0000-0003-2057-2754","full_name":"Hof, Björn"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2111.14894"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"oa":1,"type":"journal_article","date_published":"2022-01-05T00:00:00Z","language":[{"iso":"eng"}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"25152F3A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Decoding the complexity of turbulence at its origin","grant_number":"306589"},{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","grant_number":"662960"}],"oa_version":"Preprint","acknowledged_ssus":[{"_id":"M-Shop"}],"article_number":"014502","month":"01","publication":"Physical Review Letters"},{"publisher":"American Physical Society","article_type":"letter_note","quality_controlled":"1","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"article_processing_charge":"No","date_created":"2021-06-16T15:45:36Z","publication_status":"published","intvolume":"       126","title":"Coarse graining the state space of a turbulent flow using periodic orbits","_id":"9558","issue":"24","author":[{"full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312","last_name":"Yalniz","first_name":"Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425"},{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","last_name":"Hof","orcid":"0000-0003-2057-2754","full_name":"Hof, Björn"},{"orcid":"0000-0003-0423-5010","full_name":"Budanur, Nazmi B","first_name":"Nazmi B","last_name":"Budanur","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87"}],"volume":126,"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.","day":"18","arxiv":1,"doi":"10.1103/PhysRevLett.126.244502","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"}],"citation":{"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.","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>.","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>","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>","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.","short":"G. Yalniz, B. Hof, N.B. Budanur, Physical Review Letters 126 (2021).","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>."},"year":"2021","date_updated":"2023-08-08T14:08:36Z","external_id":{"arxiv":["2007.02584"],"isi":["000663310100008"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"grant_number":"662960","name":"Revisiting the Turbulence Problem Using Statistical Mechanics: Experimental Studies on Transitional and Turbulent Flows","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"oa_version":"Preprint","acknowledged_ssus":[{"_id":"ScienComp"}],"article_number":"244502","month":"06","publication":"Physical Review Letters","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2007.02584"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","related_material":{"link":[{"url":"https://ist.ac.at/en/news/turbulent-flow-simplified/","description":"News on IST Homepage","relation":"press_release"}]},"publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"oa":1,"type":"journal_article","date_published":"2021-06-18T00:00:00Z"}]