[{"acknowledgement":"We gratefully acknowledge the assistance of J. M. Lopez with DNSs at an early stage of this work. This work was partially supported by two grants from the Simons Foundation (grant nos. 662985 (N.G.) and 662960 (B.H.)) and by Ministry of Science and Technology, Taiwan (grant nos. MOST 109-2112-M-001-017-MY3 and MOST 111-2112-M-001-027-MY3 (H.-Y.S.)). Part of this work was performed using computing resources of CRIANN (Normandy, France).","corr_author":"1","publication_identifier":{"issn":["1745-2473"],"eissn":["1745-2481"]},"external_id":{"isi":["001232300600001"]},"project":[{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960"}],"type":"journal_article","month":"08","abstract":[{"text":"The onset of turbulence in pipe flow has defied detailed understanding ever since the first observations of the spatially heterogeneous nature of the transition. Recent theoretical studies and experiments in simpler, shear-driven flows suggest that the onset of turbulence is a directed-percolation non-equilibrium phase transition, but whether these findings are generic and also apply to open or pressure-driven flows is unknown. In pipe flow, the extremely long time scales near the transition make direct observations of critical behaviour virtually impossible. Here we find a technical solution to that limitation and show that the universality class of the transition is directed percolation, from which a jammed phase of puffs emerges above the critical point. Our method is to experimentally characterize all pairwise interactions between localized patches of turbulence puffs and use these interactions as input for renormalization group and computer simulations of minimal models that extrapolate to long length and time scales. The strong interactions in the jamming regime enable us to explicitly measure the turbulent fraction and confirm model predictions. Our work shows that directed-percolation scaling applies beyond simple closed shear flows and underscores how statistical mechanics can lead to profound, quantitative and predictive insights on turbulent flows and their phases.","lang":"eng"}],"oa_version":"None","doi":"10.1038/s41567-024-02513-0","date_created":"2024-06-09T22:01:03Z","article_processing_charge":"No","title":"Directed percolation and puff jamming near the transition to pipe turbulence","department":[{"_id":"BjHo"}],"intvolume":"        20","publication_status":"published","language":[{"iso":"eng"}],"date_published":"2024-08-01T00:00:00Z","_id":"17128","isi":1,"article_type":"original","quality_controlled":"1","volume":20,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","citation":{"chicago":"Lemoult, Grégoire M, Mukund Vasudevan, Hong Yan Shih, Gaute Linga, Joachim Mathiesen, Nigel Goldenfeld, and Björn Hof. “Directed Percolation and Puff Jamming near the Transition to Pipe Turbulence.” <i>Nature Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1038/s41567-024-02513-0\">https://doi.org/10.1038/s41567-024-02513-0</a>.","ista":"Lemoult GM, Vasudevan M, Shih HY, Linga G, Mathiesen J, Goldenfeld N, Hof B. 2024. Directed percolation and puff jamming near the transition to pipe turbulence. Nature Physics. 20, 1339–1345.","short":"G.M. Lemoult, M. Vasudevan, H.Y. Shih, G. Linga, J. Mathiesen, N. Goldenfeld, B. Hof, Nature Physics 20 (2024) 1339–1345.","ama":"Lemoult GM, Vasudevan M, Shih HY, et al. Directed percolation and puff jamming near the transition to pipe turbulence. <i>Nature Physics</i>. 2024;20:1339-1345. doi:<a href=\"https://doi.org/10.1038/s41567-024-02513-0\">10.1038/s41567-024-02513-0</a>","ieee":"G. M. Lemoult <i>et al.</i>, “Directed percolation and puff jamming near the transition to pipe turbulence,” <i>Nature Physics</i>, vol. 20. Springer Nature, pp. 1339–1345, 2024.","apa":"Lemoult, G. M., Vasudevan, M., Shih, H. Y., Linga, G., Mathiesen, J., Goldenfeld, N., &#38; Hof, B. (2024). Directed percolation and puff jamming near the transition to pipe turbulence. <i>Nature Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41567-024-02513-0\">https://doi.org/10.1038/s41567-024-02513-0</a>","mla":"Lemoult, Grégoire M., et al. “Directed Percolation and Puff Jamming near the Transition to Pipe Turbulence.” <i>Nature Physics</i>, vol. 20, Springer Nature, 2024, pp. 1339–45, doi:<a href=\"https://doi.org/10.1038/s41567-024-02513-0\">10.1038/s41567-024-02513-0</a>."},"page":"1339-1345","publication":"Nature Physics","status":"public","publisher":"Springer Nature","scopus_import":"1","date_updated":"2025-09-08T07:50:20Z","author":[{"id":"4787FE80-F248-11E8-B48F-1D18A9856A87","first_name":"Grégoire M","last_name":"Lemoult","full_name":"Lemoult, Grégoire M"},{"last_name":"Vasudevan","first_name":"Mukund","full_name":"Vasudevan, Mukund","id":"3C5A959A-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Shih","first_name":"Hong Yan","full_name":"Shih, Hong Yan"},{"full_name":"Linga, Gaute","first_name":"Gaute","last_name":"Linga"},{"first_name":"Joachim","last_name":"Mathiesen","full_name":"Mathiesen, Joachim"},{"full_name":"Goldenfeld, Nigel","last_name":"Goldenfeld","first_name":"Nigel"},{"last_name":"Hof","first_name":"Björn","full_name":"Hof, Björn","orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87"}],"year":"2024"},{"publication":"Physical Review Letters","status":"public","citation":{"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>","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>.","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>","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.","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).","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>."},"article_number":"014502","publisher":"American Physical Society","scopus_import":"1","ec_funded":1,"date_updated":"2024-10-22T11:08:41Z","acknowledged_ssus":[{"_id":"M-Shop"}],"author":[{"id":"2C9AF1C2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1740-7635","full_name":"Klotz, Lukasz","last_name":"Klotz","first_name":"Lukasz"},{"full_name":"Lemoult, Grégoire M","last_name":"Lemoult","first_name":"Grégoire M","id":"4787FE80-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avila, Kerstin","last_name":"Avila","first_name":"Kerstin"},{"orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","last_name":"Hof","full_name":"Hof, Björn"}],"year":"2022","article_type":"original","quality_controlled":"1","oa":1,"volume":128,"issue":"1","day":"05","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       128","publication_status":"published","pmid":1,"language":[{"iso":"eng"}],"date_published":"2022-01-05T00:00:00Z","isi":1,"_id":"10654","publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"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","corr_author":"1","type":"journal_article","month":"01","arxiv":1,"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"}],"external_id":{"isi":["000748271700010"],"arxiv":["2111.14894"],"pmid":["35061458"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"25152F3A-B435-11E9-9278-68D0E5697425","name":"Decoding the complexity of turbulence at its origin","grant_number":"306589","call_identifier":"FP7"},{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960","name":"Revisiting the Turbulence Problem Using Statistical Mechanics"}],"title":"Phase transition to turbulence in spatially extended shear flows","oa_version":"Preprint","date_created":"2022-01-23T23:01:28Z","doi":"10.1103/PhysRevLett.128.014502","article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/2111.14894","open_access":"1"}],"department":[{"_id":"BjHo"}]},{"scopus_import":"1","publisher":"American Physical Society","status":"public","publication":"Physical Review Fluids","citation":{"ista":"Klotz L, Lemoult GM, Frontczak I, Tuckerman L, Wesfreid J. 2017. Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence. Physical Review Fluids. 2(4), 043904.","short":"L. Klotz, G.M. Lemoult, I. Frontczak, L. Tuckerman, J. Wesfreid, Physical Review Fluids 2 (2017).","chicago":"Klotz, Lukasz, Grégoire M Lemoult, Idalia Frontczak, Laurette Tuckerman, and José Wesfreid. “Couette-Poiseuille Flow Experiment with Zero Mean Advection Velocity: Subcritical Transition to Turbulence.” <i>Physical Review Fluids</i>. American Physical Society, 2017. <a href=\"https://doi.org/10.1103/PhysRevFluids.2.043904\">https://doi.org/10.1103/PhysRevFluids.2.043904</a>.","ieee":"L. Klotz, G. M. Lemoult, I. Frontczak, L. Tuckerman, and J. Wesfreid, “Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence,” <i>Physical Review Fluids</i>, vol. 2, no. 4. American Physical Society, 2017.","mla":"Klotz, Lukasz, et al. “Couette-Poiseuille Flow Experiment with Zero Mean Advection Velocity: Subcritical Transition to Turbulence.” <i>Physical Review Fluids</i>, vol. 2, no. 4, 043904, American Physical Society, 2017, doi:<a href=\"https://doi.org/10.1103/PhysRevFluids.2.043904\">10.1103/PhysRevFluids.2.043904</a>.","apa":"Klotz, L., Lemoult, G. M., Frontczak, I., Tuckerman, L., &#38; Wesfreid, J. (2017). Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence. <i>Physical Review Fluids</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevFluids.2.043904\">https://doi.org/10.1103/PhysRevFluids.2.043904</a>","ama":"Klotz L, Lemoult GM, Frontczak I, Tuckerman L, Wesfreid J. Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence. <i>Physical Review Fluids</i>. 2017;2(4). doi:<a href=\"https://doi.org/10.1103/PhysRevFluids.2.043904\">10.1103/PhysRevFluids.2.043904</a>"},"article_number":"043904","year":"2017","author":[{"first_name":"Lukasz","last_name":"Klotz","full_name":"Klotz, Lukasz","orcid":"0000-0003-1740-7635","id":"2C9AF1C2-F248-11E8-B48F-1D18A9856A87"},{"id":"4787FE80-F248-11E8-B48F-1D18A9856A87","full_name":"Lemoult, Grégoire M","first_name":"Grégoire M","last_name":"Lemoult"},{"first_name":"Idalia","last_name":"Frontczak","full_name":"Frontczak, Idalia"},{"first_name":"Laurette","last_name":"Tuckerman","full_name":"Tuckerman, Laurette"},{"last_name":"Wesfreid","first_name":"José","full_name":"Wesfreid, José"}],"date_updated":"2025-09-18T09:49:18Z","quality_controlled":"1","oa":1,"day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":2,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"         2","publist_id":"7306","_id":"513","isi":1,"date_published":"2017-04-01T00:00:00Z","abstract":[{"lang":"eng","text":"We present an experimental setup that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We obtain experimental results in the transitional regime for this flow. Using flow visualization, we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures are nearly stationary. We distinguish two regions of the turbulent spot: the active turbulent core, which is characterized by waviness of the streaks similar to traveling waves, and the surrounding region, which includes in addition the weak undisturbed streaks and oblique waves at the laminar-turbulent interface. We also study the dependence of the size of these two regions on Reynolds number. Finally, we show that the traveling waves move in the downstream (Poiseuille) direction."}],"arxiv":1,"month":"04","type":"journal_article","external_id":{"arxiv":["1704.02619"],"isi":["000400249900003"]},"department":[{"_id":"BjHo"}],"title":"Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.02619"}],"article_processing_charge":"No","date_created":"2018-12-11T11:46:54Z","doi":"10.1103/PhysRevFluids.2.043904","oa_version":"Preprint"},{"issue":"3","volume":12,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"15","quality_controlled":"1","date_updated":"2025-09-18T11:11:31Z","author":[{"id":"4787FE80-F248-11E8-B48F-1D18A9856A87","full_name":"Lemoult, Grégoire M","first_name":"Grégoire M","last_name":"Lemoult"},{"first_name":"Liang","last_name":"Shi","full_name":"Shi, Liang","id":"374A3F1A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avila, Kerstin","last_name":"Avila","first_name":"Kerstin"},{"full_name":"Jalikop, Shreyas V","first_name":"Shreyas V","last_name":"Jalikop","id":"44A1D772-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Avila, Marc","first_name":"Marc","last_name":"Avila"},{"orcid":"0000-0003-2057-2754","id":"3A374330-F248-11E8-B48F-1D18A9856A87","full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn"}],"year":"2016","citation":{"ista":"Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. 2016. Directed percolation phase transition to sustained turbulence in Couette flow. Nature Physics. 12(3), 254–258.","short":"G.M. Lemoult, L. Shi, K. Avila, S.V. Jalikop, M. Avila, B. Hof, Nature Physics 12 (2016) 254–258.","chicago":"Lemoult, Grégoire M, Liang Shi, Kerstin Avila, Shreyas V Jalikop, Marc Avila, and Björn Hof. “Directed Percolation Phase Transition to Sustained Turbulence in Couette Flow.” <i>Nature Physics</i>. Nature Publishing Group, 2016. <a href=\"https://doi.org/10.1038/nphys3675\">https://doi.org/10.1038/nphys3675</a>.","mla":"Lemoult, Grégoire M., et al. “Directed Percolation Phase Transition to Sustained Turbulence in Couette Flow.” <i>Nature Physics</i>, vol. 12, no. 3, Nature Publishing Group, 2016, pp. 254–58, doi:<a href=\"https://doi.org/10.1038/nphys3675\">10.1038/nphys3675</a>.","ama":"Lemoult GM, Shi L, Avila K, Jalikop SV, Avila M, Hof B. Directed percolation phase transition to sustained turbulence in Couette flow. <i>Nature Physics</i>. 2016;12(3):254-258. doi:<a href=\"https://doi.org/10.1038/nphys3675\">10.1038/nphys3675</a>","ieee":"G. M. Lemoult, L. Shi, K. Avila, S. V. Jalikop, M. Avila, and B. Hof, “Directed percolation phase transition to sustained turbulence in Couette flow,” <i>Nature Physics</i>, vol. 12, no. 3. Nature Publishing Group, pp. 254–258, 2016.","apa":"Lemoult, G. M., Shi, L., Avila, K., Jalikop, S. V., Avila, M., &#38; Hof, B. (2016). Directed percolation phase transition to sustained turbulence in Couette flow. <i>Nature Physics</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/nphys3675\">https://doi.org/10.1038/nphys3675</a>"},"page":"254 - 258","status":"public","publication":"Nature Physics","publisher":"Nature Publishing Group","scopus_import":"1","ec_funded":1,"oa_version":"None","doi":"10.1038/nphys3675","date_created":"2018-12-11T11:52:21Z","article_processing_charge":"No","title":"Directed percolation phase transition to sustained turbulence in Couette flow","department":[{"_id":"BjHo"}],"acknowledgement":"We thank P. Maier for providing valuable ideas and supporting us in the technical aspects. Discussions with D. Barkley, Y. Duguet, B. Eckhart, N. Goldenfeld, P. Manneville and K. Takeuchi are gratefully acknowledged. We acknowledge the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. L.S. and B.H. acknowledge research funding by Deutsche Forschungsgemeinschaft (DFG) under Grant No. SFB 963/1 (project A8). Numerical simulations were performed thanks to the CPU time allocations of JUROPA in Juelich Supercomputing Center (project HGU17) and of the Max Planck Computing and Data Facility (Garching, Germany). Excellent technical support from M. Rampp on the hybrid code nsCouette is appreciated.","external_id":{"isi":["000371505200019"]},"project":[{"grant_number":"306589","name":"Decoding the complexity of turbulence at its origin","_id":"25152F3A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"2511D90C-B435-11E9-9278-68D0E5697425","grant_number":"SFB 963  TP A8","name":"Astrophysical instability of currents and turbulences"}],"month":"02","type":"journal_article","abstract":[{"lang":"eng","text":"Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature, yet characterizing the transition that gives rise to turbulence in basic shear flows has remained an elusive task. Although, in recent studies, critical points marking the onset of sustained turbulence have been determined for several such flows, the physical nature of the transition could not be fully explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second-order phase transition and falls into the directed percolation universality class. Consequently, the complex laminar–turbulent patterns distinctive for the onset of turbulence in shear flows result from short-range interactions of turbulent domains and are characterized by universal critical exponents. More generally, our study demonstrates that even high-dimensional systems far from equilibrium such as turbulence exhibit universality at onset and that here the collective dynamics obeys simple rules."}],"date_published":"2016-02-15T00:00:00Z","_id":"1494","isi":1,"publist_id":"5685","intvolume":"        12","publication_status":"published","language":[{"iso":"eng"}]},{"publist_id":"5485","intvolume":"       526","publication_status":"published","language":[{"iso":"eng"}],"date_published":"2015-10-21T00:00:00Z","_id":"1664","isi":1,"acknowledgement":"We acknowledge the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. B.S. acknowledges financial support from the Chinese State Scholarship Fund under grant number 2010629145. B.S. acknowledges support from the International Max Planck Research School for the Physics of Biological and Complex Systems and the Göttingen Graduate School for Neurosciences and Molecular Biosciences. We acknowledge computing resources from GWDG (Gesellschaft für wissenschaftliche Datenverarbeitung Göttingen) and the Jülich Supercomputing Centre (grant HGU16) where the simulations were performed.","corr_author":"1","external_id":{"isi":["000364026100045"],"arxiv":["1510.09143"]},"project":[{"_id":"25152F3A-B435-11E9-9278-68D0E5697425","name":"Decoding the complexity of turbulence at its origin","grant_number":"306589","call_identifier":"FP7"}],"type":"journal_article","arxiv":1,"month":"10","abstract":[{"text":"Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.","lang":"eng"}],"oa_version":"Preprint","doi":"10.1038/nature15701","date_created":"2018-12-11T11:53:20Z","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1510.09143"}],"title":"The rise of fully turbulent flow","department":[{"_id":"BjHo"}],"page":"550 - 553","citation":{"ieee":"D. Barkley, B. Song, M. Vasudevan, G. M. Lemoult, M. Avila, and B. Hof, “The rise of fully turbulent flow,” <i>Nature</i>, vol. 526, no. 7574. Nature Publishing Group, pp. 550–553, 2015.","ama":"Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. The rise of fully turbulent flow. <i>Nature</i>. 2015;526(7574):550-553. doi:<a href=\"https://doi.org/10.1038/nature15701\">10.1038/nature15701</a>","apa":"Barkley, D., Song, B., Vasudevan, M., Lemoult, G. M., Avila, M., &#38; Hof, B. (2015). The rise of fully turbulent flow. <i>Nature</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/nature15701\">https://doi.org/10.1038/nature15701</a>","mla":"Barkley, Dwight, et al. “The Rise of Fully Turbulent Flow.” <i>Nature</i>, vol. 526, no. 7574, Nature Publishing Group, 2015, pp. 550–53, doi:<a href=\"https://doi.org/10.1038/nature15701\">10.1038/nature15701</a>.","ista":"Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. 2015. The rise of fully turbulent flow. Nature. 526(7574), 550–553.","chicago":"Barkley, Dwight, Baofang Song, Mukund Vasudevan, Grégoire M Lemoult, Marc Avila, and Björn Hof. “The Rise of Fully Turbulent Flow.” <i>Nature</i>. Nature Publishing Group, 2015. <a href=\"https://doi.org/10.1038/nature15701\">https://doi.org/10.1038/nature15701</a>.","short":"D. Barkley, B. Song, M. Vasudevan, G.M. Lemoult, M. Avila, B. 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