{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T09:24:25Z","timestamp":1785489865305,"version":"3.56.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"7574","license":[{"start":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T00:00:00Z","timestamp":1443657600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1038\/nature15701","type":"journal-article","created":{"date-parts":[[2015,10,20]],"date-time":"2015-10-20T16:19:24Z","timestamp":1445357964000},"page":"550-553","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":171,"title":["The rise of fully turbulent flow"],"prefix":"10.1038","volume":"526","author":[{"given":"Dwight","family":"Barkley","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baofang","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vasudevan","family":"Mukund","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gr\u00e9goire","family":"Lemoult","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc","family":"Avila","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bj\u00f6rn","family":"Hof","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,10,21]]},"reference":[{"key":"BFnature15701_CR1","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1098\/rstl.1883.0029","volume":"174","author":"O Reynolds","year":"1883","unstructured":"Reynolds, O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. A 174, 935\u2013982 (1883)","journal-title":"Phil. Trans. R. Soc. Lond. A"},{"key":"BFnature15701_CR2","first-page":"229","volume-title":"M\u00e9canique de la Turbulence","author":"D Coles","year":"1962","unstructured":"Coles, D. Interfaces and intermittency in turbulent shear flow. In M\u00e9canique de la Turbulence 229 (\u00c9ditions du Centre National de la Recherche Scientifique, 1962)"},{"key":"BFnature15701_CR3","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1017\/S0022112073001576","volume":"59","author":"IJ Wygnanski","year":"1973","unstructured":"Wygnanski, I. J. & Champagne, F. H. On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281\u2013335 (1973)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR4","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/0167-2789(86)90134-X","volume":"23","author":"KR Sreenivasan","year":"1986","unstructured":"Sreenivasan, K. R. & Ramshankar, R. Transition intermittency in open flows, and intermittency routes to chaos. Physica D 23, 246\u2013258 (1986)","journal-title":"Physica D"},{"key":"BFnature15701_CR5","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1017\/S0022112008003315","volume":"614","author":"M Nishi","year":"2008","unstructured":"Nishi, M., \u00dcnsal, B., Durst, F. & Biswas, G. Laminar-to-turbulent transition of pipe flows through puffs and slugs. J. Fluid Mech. 614, 425\u2013446 (2008)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1146\/annurev-fluid-122109-160652","volume":"43","author":"T Mullin","year":"2011","unstructured":"Mullin, T. Experimental studies of transition to turbulence in a pipe. Annu. Rev. Fluid Mech. 43, 1\u201324 (2011)","journal-title":"Annu. Rev. Fluid Mech."},{"key":"BFnature15701_CR7","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1126\/science.1203223","volume":"333","author":"K Avila","year":"2011","unstructured":"Avila, K. et al. The onset of turbulence in pipe flow. Science 333, 192\u2013196 (2011)","journal-title":"Science"},{"key":"BFnature15701_CR8","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1017\/CBO9780511840531","volume-title":"Turbulent Flows","author":"SB Pope","year":"2000","unstructured":"Pope, S. B. Turbulent Flows Ch. 7 264\u2013332 (Cambridge Univ. Press, 2000)"},{"key":"BFnature15701_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-85829-1","volume-title":"Boundary-Layer Theory","author":"H Schlichting","year":"2000","unstructured":"Schlichting, H. & Gersten, K. Boundary-Layer Theory 8th edn (Springer, 2000)"},{"key":"BFnature15701_CR10","doi-asserted-by":"publisher","first-page":"490","DOI":"10.2514\/8.2010","volume":"18","author":"HW Emmons","year":"1951","unstructured":"Emmons, H. W. The laminar-turbulent transition in a boundary layer\u2014part I. J. Aeronaut. Sci. 18, 490\u2013498 (1951)","journal-title":"J. Aeronaut. Sci."},{"key":"BFnature15701_CR11","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1017\/S0022112065000241","volume":"21","author":"D Coles","year":"1965","unstructured":"Coles, D. Transition in circular Couette flow. J. Fluid Mech. 21, 385\u2013425 (1965)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR12","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1017\/S0022112091003130","volume":"229","author":"A Lundbladh","year":"1991","unstructured":"Lundbladh, A. & Johansson, A. V. Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499\u2013516 (1991)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR13","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1017\/S0022112092001046","volume":"235","author":"N Tillmark","year":"1992","unstructured":"Tillmark, N. & Alfredsson, P. H. Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89\u2013102 (1992)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR14","doi-asserted-by":"publisher","first-page":"3755","DOI":"10.1063\/1.1508796","volume":"14","author":"A Cros","year":"2002","unstructured":"Cros, A. & Le Gal, P. Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14, 3755\u20133765 (2002)","journal-title":"Phys. Fluids"},{"key":"BFnature15701_CR15","doi-asserted-by":"publisher","first-page":"R1","DOI":"10.1017\/jfm.2013.388","volume":"731","author":"G Lemoult","year":"2013","unstructured":"Lemoult, G., Aider, J.-L. & Wesfreid, J. E. Turbulent spots in a channel: large-scale flow and self-sustainability. J. Fluid Mech. 731, R1 (2013)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR16","doi-asserted-by":"publisher","first-page":"8091","DOI":"10.1073\/pnas.0909560107","volume":"107","author":"D Moxey","year":"2010","unstructured":"Moxey, D. & Barkley, D. Distinct large-scale turbulent-laminar states in transitional pipe flow. Proc. Natl Acad. Sci. USA 107, 8091\u20138096 (2010)","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"BFnature15701_CR17","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1017\/jfm.2011.189","volume":"681","author":"D Samanta","year":"2011","unstructured":"Samanta, D., de Lozar, A. & Hof, B. Experimental investigation of laminar turbulent intermittency in pipe flow. J. Fluid Mech. 681, 193\u2013204 (2011)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR18","doi-asserted-by":"publisher","first-page":"1491","DOI":"10.1126\/science.1186091","volume":"327","author":"B Hof","year":"2010","unstructured":"Hof, B., De Lozar, A., Avila, M., Tu, X. & Schneider, T. Eliminating turbulence in spatially intermittent flows. Science 327, 1491\u20131494 (2010)","journal-title":"Science"},{"key":"BFnature15701_CR19","unstructured":"Lindgren, E. R. The transition process and other phenomena in viscous flow. Ark. Fys. 12 (1957)"},{"key":"BFnature15701_CR20","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1017\/S0022112010003435","volume":"663","author":"Y Duguet","year":"2010","unstructured":"Duguet, Y., Willis, A. P. & Kerswell, R. R. Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663, 180\u2013208 (2010)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR21","doi-asserted-by":"publisher","first-page":"035304","DOI":"10.1103\/PhysRevE.84.035304","volume":"84","author":"M Sipos","year":"2011","unstructured":"Sipos, M. & Goldenfeld, N. Directed percolation describes lifetime and growth of turbulent puffs and slugs. Phys. Rev. E 84, 035304 (2011)","journal-title":"Phys. Rev. E"},{"key":"BFnature15701_CR22","doi-asserted-by":"publisher","first-page":"016309","DOI":"10.1103\/PhysRevE.84.016309","volume":"84","author":"D Barkley","year":"2011","unstructured":"Barkley, D. Simplifying the complexity of pipe flow. Phys. Rev. E 84, 016309 (2011)","journal-title":"Phys. Rev. E"},{"key":"BFnature15701_CR23","doi-asserted-by":"publisher","first-page":"032001","DOI":"10.1088\/1742-6596\/318\/3\/032001","volume":"318","author":"D Barkley","year":"2011","unstructured":"Barkley, D. Modeling the transition to turbulence in shear flows. J. Phys. Conf. Ser. 318, 032001 (2011)","journal-title":"J. Phys. Conf. Ser."},{"key":"BFnature15701_CR24","first-page":"1E27","volume":"29","author":"D Barkley","year":"2012","unstructured":"Barkley, D. Pipe flow as an excitable medium. Rev. Cub. Fis. 29, 1E27 (2012)","journal-title":"Rev. Cub. Fis."},{"key":"BFnature15701_CR25","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1137\/0142077","volume":"42","author":"J Rinzel","year":"1982","unstructured":"Rinzel, J. & Terman, D. Propagation phenomena in a bistable reaction-diffusion system. SIAM J. Appl. Math. 42, 1111\u20131137 (1982)","journal-title":"SIAM J. Appl. Math."},{"key":"BFnature15701_CR26","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/0167-2789(88)90062-0","volume":"32","author":"J Tyson","year":"1988","unstructured":"Tyson, J. & Keener, J. Singular perturbation theory of traveling waves in excitable media (a review). Physica D 32, 327\u2013361 (1988)","journal-title":"Physica D"},{"key":"BFnature15701_CR27","doi-asserted-by":"publisher","first-page":"063012","DOI":"10.1103\/PhysRevE.87.063012","volume":"87","author":"M Avila","year":"2013","unstructured":"Avila, M. & Hof, B. Nature of laminar-turbulence intermittency in shear flows. Phys. Rev. E 87, 063012 (2013)","journal-title":"Phys. Rev. E"},{"key":"BFnature15701_CR28","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1146\/annurev.fluid.39.050905.110308","volume":"39","author":"B Eckhardt","year":"2007","unstructured":"Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447\u2013468 (2007)","journal-title":"Annu. Rev. Fluid Mech."},{"key":"BFnature15701_CR29","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1017\/S002211200800267X","volume":"611","author":"J Gibson","year":"2008","unstructured":"Gibson, J., Halcrow, J. & Cvitanovi\u0107, P. Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107\u2013130 (2008)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR30","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1146\/annurev-fluid-120710-101228","volume":"44","author":"G Kawahara","year":"2012","unstructured":"Kawahara, G., Uhlmann, M. & van Veen, L. The significance of simple invariant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44, 203\u2013225 (2012)","journal-title":"Annu. Rev. Fluid Mech."},{"key":"BFnature15701_CR31","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1017\/S0022112008004618","volume":"619","author":"AP Willis","year":"2009","unstructured":"Willis, A. P. & Kerswell, R. R. Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized \u2018edge\u2019 states. J. Fluid Mech. 619, 213\u2013233 (2009)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR32","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1017\/S0022112075001449","volume":"69","author":"I Wygnanski","year":"1975","unstructured":"Wygnanski, I., Sokolov, M. & Friedman, D. On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283\u2013304 (1975)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR33","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1017\/jfm.2013.127","volume":"723","author":"M Holzner","year":"2013","unstructured":"Holzner, M., Song, B., Avila, M. & Hof, B. Lagrangian approach to laminar\u2013turbulent interfaces in transitional pipe flow. J. Fluid Mech. 723, 140\u2013162 (2013)","journal-title":"J. Fluid Mech."},{"key":"BFnature15701_CR34","doi-asserted-by":"publisher","first-page":"R17","DOI":"10.1088\/0951-7715\/18\/6\/R01","volume":"18","author":"RR Kerswell","year":"2005","unstructured":"Kerswell, R. R. Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity 18, R17\u2013R44 (2005)","journal-title":"Nonlinearity"},{"key":"BFnature15701_CR35","doi-asserted-by":"publisher","first-page":"224502","DOI":"10.1103\/PhysRevLett.110.224502","volume":"110","author":"M Avila","year":"2013","unstructured":"Avila, M., Mellibovsky, F., Roland, N. & Hof, B. Streamwise-localized solutions at the onset of turbulence in pipe flow. Phys. Rev. Lett. 110, 224502 (2013)","journal-title":"Phys. Rev. Lett."},{"key":"BFnature15701_CR36","doi-asserted-by":"publisher","first-page":"164501","DOI":"10.1103\/PhysRevLett.112.164501","volume":"112","author":"M Chantry","year":"2014","unstructured":"Chantry, M., Willis, A. P. & Kerswell, R. R. Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow. Phys. Rev. Lett. 112, 164501 (2014)","journal-title":"Phys. Rev. Lett."}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.nature.com\/articles\/nature15701.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/www.nature.com\/articles\/nature15701","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/www.nature.com\/articles\/nature15701.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T17:46:34Z","timestamp":1684431994000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/nature15701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":36,"journal-issue":{"issue":"7574","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["BFnature15701"],"URL":"https:\/\/doi.org\/10.1038\/nature15701","relation":{},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]},"assertion":[{"value":"6 June 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2015","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2015","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing financial interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}