--- _id: '5996' abstract: - lang: eng text: 'In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ( ) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on . In accordance with Reynolds’ proposition, we find that at lower (here 2020), flows eventually always resume to laminar, while for higher ( ), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020 , which is in very good agreement with the recently proposed value of . The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion.' acknowledgement: ' We also thank Philipp Maier and the IST Austria workshop for theirdedicated technical support' article_processing_charge: No article_type: original author: - first_name: Mukund full_name: Vasudevan, Mukund id: 3C5A959A-F248-11E8-B48F-1D18A9856A87 last_name: Vasudevan - first_name: Björn full_name: Hof, Björn id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: ama: Vasudevan M, Hof B. The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. 2018;839:76-94. doi:10.1017/jfm.2017.923 apa: Vasudevan, M., & Hof, B. (2018). The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2017.923 chicago: Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition to Turbulence in Pipe Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2018. https://doi.org/10.1017/jfm.2017.923. ieee: M. Vasudevan and B. Hof, “The critical point of the transition to turbulence in pipe flow,” Journal of Fluid Mechanics, vol. 839. Cambridge University Press, pp. 76–94, 2018. ista: Vasudevan M, Hof B. 2018. The critical point of the transition to turbulence in pipe flow. Journal of Fluid Mechanics. 839, 76–94. mla: Vasudevan, Mukund, and Björn Hof. “The Critical Point of the Transition to Turbulence in Pipe Flow.” Journal of Fluid Mechanics, vol. 839, Cambridge University Press, 2018, pp. 76–94, doi:10.1017/jfm.2017.923. short: M. Vasudevan, B. Hof, Journal of Fluid Mechanics 839 (2018) 76–94. date_created: 2019-02-14T12:50:50Z date_published: 2018-03-25T00:00:00Z date_updated: 2023-09-19T14:37:49Z day: '25' department: - _id: BjHo doi: 10.1017/jfm.2017.923 ec_funded: 1 external_id: arxiv: - '1709.06372' isi: - '000437858300003' intvolume: ' 839' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.06372 month: '03' oa: 1 oa_version: Preprint page: 76-94 project: - _id: 25152F3A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '306589' name: Decoding the complexity of turbulence at its origin publication: Journal of Fluid Mechanics publication_identifier: eissn: - 1469-7645 issn: - 0022-1120 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: The critical point of the transition to turbulence in pipe flow type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 839 year: '2018' ... --- _id: '1664' abstract: - lang: eng 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. 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. author: - first_name: Dwight full_name: Barkley, Dwight last_name: Barkley - first_name: Baofang full_name: Song, Baofang last_name: Song - first_name: Mukund full_name: Vasudevan, Mukund id: 3C5A959A-F248-11E8-B48F-1D18A9856A87 last_name: Vasudevan - first_name: Grégoire M full_name: Lemoult, Grégoire M id: 4787FE80-F248-11E8-B48F-1D18A9856A87 last_name: Lemoult - first_name: Marc full_name: Avila, Marc last_name: Avila - first_name: Björn full_name: Hof, Björn id: 3A374330-F248-11E8-B48F-1D18A9856A87 last_name: Hof orcid: 0000-0003-2057-2754 citation: ama: Barkley D, Song B, Vasudevan M, Lemoult GM, Avila M, Hof B. The rise of fully turbulent flow. Nature. 2015;526(7574):550-553. doi:10.1038/nature15701 apa: Barkley, D., Song, B., Vasudevan, M., Lemoult, G. M., Avila, M., & Hof, B. (2015). The rise of fully turbulent flow. Nature. Nature Publishing Group. https://doi.org/10.1038/nature15701 chicago: Barkley, Dwight, Baofang Song, Mukund Vasudevan, Grégoire M Lemoult, Marc Avila, and Björn Hof. “The Rise of Fully Turbulent Flow.” Nature. Nature Publishing Group, 2015. https://doi.org/10.1038/nature15701. ieee: D. Barkley, B. Song, M. Vasudevan, G. M. Lemoult, M. Avila, and B. Hof, “The rise of fully turbulent flow,” Nature, vol. 526, no. 7574. Nature Publishing Group, pp. 550–553, 2015. 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. mla: Barkley, Dwight, et al. “The Rise of Fully Turbulent Flow.” Nature, vol. 526, no. 7574, Nature Publishing Group, 2015, pp. 550–53, doi:10.1038/nature15701. short: D. Barkley, B. Song, M. Vasudevan, G.M. Lemoult, M. Avila, B. Hof, Nature 526 (2015) 550–553. date_created: 2018-12-11T11:53:20Z date_published: 2015-10-21T00:00:00Z date_updated: 2021-01-12T06:52:22Z day: '21' department: - _id: BjHo doi: 10.1038/nature15701 ec_funded: 1 intvolume: ' 526' issue: '7574' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1510.09143 month: '10' oa: 1 oa_version: Preprint page: 550 - 553 project: - _id: 25152F3A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '306589' name: Decoding the complexity of turbulence at its origin publication: Nature publication_status: published publisher: Nature Publishing Group publist_id: '5485' quality_controlled: '1' scopus_import: 1 status: public title: The rise of fully turbulent flow type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 526 year: '2015' ...