[{"author":[{"first_name":"Mukund","id":"3C5A959A-F248-11E8-B48F-1D18A9856A87","last_name":"Vasudevan","full_name":"Vasudevan, Mukund"},{"last_name":"Paranjape","full_name":"Paranjape, Chaitanya S","first_name":"Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michael Philip","id":"0ba0f1f2-9cfe-11f0-bee6-f95318d225b0","last_name":"Sitte","full_name":"Sitte, Michael Philip"},{"first_name":"Gökhan","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","last_name":"Yalniz","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312"},{"full_name":"Hof, Björn","last_name":"Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","orcid":"0000-0003-2057-2754"}],"scopus_import":"1","file_date_updated":"2025-09-27T13:32:03Z","publication":"Nature Communications","intvolume":"        16","isi":1,"DOAJ_listed":"1","acknowledgement":"This work was supported by a grant from the Simons Foundation (662960, BH). We thank Yohann Duguet for helpful discussions, Baofang Song for the initial adaptation of openpipeflow57 to the channel geometry, and Ashley P. Willis for openpipeflow57.","file":[{"checksum":"945926ead9cde464435d456427e2869e","content_type":"application/pdf","date_updated":"2025-09-27T13:32:03Z","file_name":"s41467-025-63044-7.pdf","creator":"gyalniz","file_id":"20403","date_created":"2025-09-27T13:32:03Z","file_size":2226082,"access_level":"open_access","relation":"main_file"}],"publication_identifier":{"eissn":["2041-1723"]},"oa":1,"publication_status":"published","department":[{"_id":"BjHo"}],"external_id":{"arxiv":["2112.06537"],"isi":["001582555200041"]},"date_created":"2025-09-27T13:27:31Z","language":[{"iso":"eng"}],"corr_author":"1","volume":16,"quality_controlled":"1","license":"https://creativecommons.org/licenses/by/4.0/","abstract":[{"lang":"eng","text":"The recent classification of the onset of turbulence as a directed percolation (DP) phase transition has been applied to all major shear flows including pipe, channel, Couette and boundary layer flows. A cornerstone of the DP analogy is the memoryless (Poisson) property of turbulent sites. We here show that, for the classic case of channel flow, neither the decay nor the proliferation of turbulent stripes is memoryless. As demonstrated by a standard analysis of the respective survival curves, isolated channel stripes, in the immediate vicinity of the critical point, age. Consequently, the one to one mapping between turbulent stripes and active DP-sites is not fulfilled in this low Reynolds number regime. In addition, the interpretation of turbulence as a chaotic saddle with supertransient properties, the basis of recent theoretical progress, does not apply to individual localized stripes. The discrepancy between channel flow and the transition models established for pipe and Couette flow, illustrates that seemingly minor geometrical differences between flows can give rise to instabilities and growth mechanisms that fundamentally alter the nature of the transition to turbulence."}],"article_number":"8447","project":[{"name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960","_id":"238598C6-32DE-11EA-91FC-C7463DDC885E"}],"has_accepted_license":"1","date_published":"2025-09-26T00:00:00Z","year":"2025","oa_version":"Published Version","date_updated":"2025-12-01T12:40:27Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"26","type":"journal_article","publisher":"Springer Nature","arxiv":1,"ddc":["532"],"doi":"10.1038/s41467-025-63044-7","OA_place":"publisher","article_type":"original","OA_type":"gold","_id":"20402","title":"Aging and memory of transitional turbulence","month":"09","article_processing_charge":"Yes","citation":{"ama":"Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. Aging and memory of transitional turbulence. <i>Nature Communications</i>. 2025;16. doi:<a href=\"https://doi.org/10.1038/s41467-025-63044-7\">10.1038/s41467-025-63044-7</a>","apa":"Vasudevan, M., Paranjape, C. S., Sitte, M. P., Yalniz, G., &#38; Hof, B. (2025). Aging and memory of transitional turbulence. <i>Nature Communications</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41467-025-63044-7\">https://doi.org/10.1038/s41467-025-63044-7</a>","chicago":"Vasudevan, Mukund, Chaitanya S Paranjape, Michael Philip Sitte, Gökhan Yalniz, and Björn Hof. “Aging and Memory of Transitional Turbulence.” <i>Nature Communications</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1038/s41467-025-63044-7\">https://doi.org/10.1038/s41467-025-63044-7</a>.","ista":"Vasudevan M, Paranjape CS, Sitte MP, Yalniz G, Hof B. 2025. Aging and memory of transitional turbulence. Nature Communications. 16, 8447.","mla":"Vasudevan, Mukund, et al. “Aging and Memory of Transitional Turbulence.” <i>Nature Communications</i>, vol. 16, 8447, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1038/s41467-025-63044-7\">10.1038/s41467-025-63044-7</a>.","short":"M. Vasudevan, C.S. Paranjape, M.P. Sitte, G. Yalniz, B. Hof, Nature Communications 16 (2025).","ieee":"M. Vasudevan, C. S. Paranjape, M. P. Sitte, G. Yalniz, and B. Hof, “Aging and memory of transitional turbulence,” <i>Nature Communications</i>, vol. 16. Springer Nature, 2025."},"PlanS_conform":"1"},{"volume":131,"quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"article_number":"034002","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"external_id":{"isi":["001052929900004"],"pmid":["37540883"],"arxiv":["2306.05098"]},"date_created":"2023-07-24T09:43:59Z","language":[{"iso":"eng"}],"corr_author":"1","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.).","pmid":1,"oa":1,"publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2306.05098"}],"publication":"Physical Review Letters","scopus_import":"1","author":[{"id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87","first_name":"Chaitanya S","last_name":"Paranjape","full_name":"Paranjape, Chaitanya S"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","first_name":"Gökhan","full_name":"Yalniz, Gökhan","last_name":"Yalniz","orcid":"0000-0002-8490-9312"},{"first_name":"Yohann","last_name":"Duguet","full_name":"Duguet, Yohann"},{"orcid":"0000-0003-0423-5010","last_name":"Budanur","full_name":"Budanur, Nazmi B","id":"3EA1010E-F248-11E8-B48F-1D18A9856A87","first_name":"Nazmi B"},{"full_name":"Hof, Björn","last_name":"Hof","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","orcid":"0000-0003-2057-2754"}],"keyword":["General Physics and Astronomy"],"intvolume":"       131","isi":1,"_id":"13274","title":"Direct path from turbulence to time-periodic solutions","month":"07","article_processing_charge":"No","citation":{"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>.","short":"C.S. Paranjape, G. Yalniz, Y. Duguet, N.B. Budanur, B. Hof, Physical Review Letters 131 (2023).","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>","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>.","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."},"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19684"}]},"arxiv":1,"doi":"10.1103/physrevlett.131.034002","article_type":"original","status":"public","day":"21","publisher":"American Physical Society","type":"journal_article","issue":"3","project":[{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","grant_number":"662960","name":"Revisiting the Turbulence Problem Using Statistical Mechanics"}],"date_published":"2023-07-21T00:00:00Z","oa_version":"Preprint","year":"2023","date_updated":"2026-04-07T11:47:05Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"day":"25","type":"journal_article","publisher":"Cambridge University Press","tmp":{"image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode"},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","year":"2020","date_updated":"2025-07-10T11:55:03Z","date_published":"2020-08-25T00:00:00Z","has_accepted_license":"1","citation":{"chicago":"Paranjape, Chaitanya S, Yohann Duguet, and Björn Hof. “Oblique Stripe Solutions of Channel Flow.” <i>Journal of Fluid Mechanics</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/jfm.2020.322\">https://doi.org/10.1017/jfm.2020.322</a>.","ista":"Paranjape CS, Duguet Y, Hof B. 2020. Oblique stripe solutions of channel flow. Journal of Fluid Mechanics. 897, A7.","ama":"Paranjape CS, Duguet Y, Hof B. Oblique stripe solutions of channel flow. <i>Journal of Fluid Mechanics</i>. 2020;897. doi:<a href=\"https://doi.org/10.1017/jfm.2020.322\">10.1017/jfm.2020.322</a>","apa":"Paranjape, C. S., Duguet, Y., &#38; Hof, B. (2020). Oblique stripe solutions of channel flow. <i>Journal of Fluid Mechanics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/jfm.2020.322\">https://doi.org/10.1017/jfm.2020.322</a>","ieee":"C. S. Paranjape, Y. Duguet, and B. Hof, “Oblique stripe solutions of channel flow,” <i>Journal of Fluid Mechanics</i>, vol. 897. Cambridge University Press, 2020.","short":"C.S. Paranjape, Y. Duguet, B. Hof, Journal of Fluid Mechanics 897 (2020).","mla":"Paranjape, Chaitanya S., et al. “Oblique Stripe Solutions of Channel Flow.” <i>Journal of Fluid Mechanics</i>, vol. 897, A7, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/jfm.2020.322\">10.1017/jfm.2020.322</a>."},"article_processing_charge":"Yes (via OA deal)","title":"Oblique stripe solutions of channel flow","month":"08","_id":"8043","doi":"10.1017/jfm.2020.322","article_type":"original","ddc":["530"],"oa":1,"publication_identifier":{"eissn":["1469-7645"],"issn":["0022-1120"]},"acknowledgement":"The authors thank S. Zammert and B. Budanur for useful discussions. J. F. Gibson is gratefully acknowledged for the development and the maintenance of the code Channelflow. Y.D. would like to thank P. Schlatter and D. S. Henningson for an early collaboration on a similar topic in the case of plane Couette flow during the years 2008–2013.","file":[{"access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:48:08Z","checksum":"3f487bf6d9286787096306eaa18702e8","content_type":"application/pdf","file_size":767873,"file_name":"2020_JournalOfFluidMech_Paranjape.pdf","creator":"cziletti","date_created":"2020-06-30T08:37:37Z","file_id":"8070"}],"intvolume":"       897","isi":1,"file_date_updated":"2020-07-14T12:48:08Z","scopus_import":"1","publication":"Journal of Fluid Mechanics","author":[{"last_name":"Paranjape","full_name":"Paranjape, Chaitanya S","first_name":"Chaitanya S","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yohann","last_name":"Duguet","full_name":"Duguet, Yohann"},{"full_name":"Hof, Björn","last_name":"Hof","first_name":"Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754"}],"abstract":[{"lang":"eng","text":"With decreasing Reynolds number, Re, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of Re lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain."}],"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","article_number":"A7","quality_controlled":"1","volume":897,"language":[{"iso":"eng"}],"corr_author":"1","external_id":{"isi":["000539132300001"]},"department":[{"_id":"BjHo"}],"date_created":"2020-06-29T07:59:35Z","publication_status":"published"},{"date_created":"2019-10-22T12:08:43Z","department":[{"_id":"BjHo"}],"language":[{"iso":"eng"}],"corr_author":"1","degree_awarded":"PhD","publication_status":"published","supervisor":[{"last_name":"Hof","full_name":"Hof, Björn","id":"3A374330-F248-11E8-B48F-1D18A9856A87","first_name":"Björn","orcid":"0000-0003-2057-2754"}],"abstract":[{"lang":"eng","text":"In many shear flows like pipe flow, plane Couette flow, plane Poiseuille flow,  etc. turbulence emerges subcritically. Here, when subjected to strong enough perturbations, the flow becomes turbulent in spite of the laminar base flow being linearly stable.  The nature of this instability has puzzled the scientific community for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally intermittent.  In pipe flow the localized turbulent structures are referred to as puffs and in planar flows like plane Couette and channel flow, patches arise in the form of localized oblique bands. In this thesis, we study the onset of turbulence in channel flow in direct numerical simulations from a dynamical system theory perspective, as well as by performing experiments in a large aspect ratio channel.\r\n\r\nThe aim of the experimental work is to determine the critical Reynolds number where turbulence first becomes sustained. Recently, the onset of turbulence has been described in analogy to absorbing state phase transition (i.e. directed percolation). In particular, it has been shown that the critical point can be estimated from the competition between spreading and decay processes. Here, by performing experiments, we identify the mechanisms underlying turbulence proliferation in channel flow and find the critical Reynolds number, above which turbulence becomes sustained. Above the critical point, the continuous growth at the tip of the stripes outweighs the stochastic shedding of turbulent patches at the tail and the stripes expand. For growing stripes, the probability to decay decreases while the probability of stripe splitting increases. Consequently, and unlike for the puffs in pipe flow, neither of these two processes is time-independent i.e. memoryless. Coupling between stripe expansion and creation of new stripes via splitting leads to a significantly lower critical point ($Re_c=670+/-10$) than most earlier studies suggest.  \r\n\r\nWhile the above approach sheds light on how turbulence first becomes sustained, it provides no insight into the origin of the stripes themselves. In the numerical part of the thesis we investigate how turbulent stripes form from invariant solutions of the Navier-Stokes equations. The origin of these turbulent stripes can be identified by applying concepts from the dynamical system theory. In doing so, we identify the exact coherent structures underlying stripes and their bifurcations and how they give rise to the turbulent attractor in phase space. We first report a family of localized nonlinear traveling wave solutions of the Navier-Stokes equations in channel flow. These solutions show structural similarities with turbulent stripes in experiments like obliqueness, quasi-streamwise streaks and vortices, etc. A parametric study of these traveling wave solution is performed, with parameters like Reynolds number, stripe tilt angle and domain size, including the stability of the solutions. These solutions emerge through saddle-node bifurcations and form a phase space skeleton for the turbulent stripes observed in the experiments. The lower branches of these TW solutions at different tilt angles undergo Hopf bifurcation and new solutions branches of relative periodic orbits emerge. These RPO solutions do not belong to the same family and therefore the routes to chaos for different angles are different.  \r\n\r\nIn shear flows, turbulence at onset is transient in nature.  Consequently,turbulence can not be tracked to lower Reynolds numbers, where the dynamics may simplify. Before this happens, turbulence becomes short-lived and laminarizes. In the last part of the thesis, we show that using numerical simulations we can continue turbulent stripes in channel flow past the 'relaminarization barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies and the fluctuations are no longer stochastic and the stripe settles down to a relative periodic orbit. This relative periodic orbit originates from the aforementioned traveling wave solutions. Starting from the relative periodic orbit, a small increase in speed i.e. Reynolds number gives rise to chaos and the attractor dimension sharply increases in contrast to the classical transition scenario where the instabilities affect the flow globally and give rise to much more gradual route to turbulence."}],"author":[{"full_name":"Paranjape, Chaitanya S","last_name":"Paranjape","id":"3D85B7C4-F248-11E8-B48F-1D18A9856A87","first_name":"Chaitanya S"}],"file_date_updated":"2020-07-14T12:47:46Z","keyword":["Instabilities","Turbulence","Nonlinear dynamics"],"file":[{"date_updated":"2020-07-14T12:47:46Z","checksum":"7ba298ba0ce7e1d11691af6b8eaf0a0a","content_type":"application/zip","file_size":45828099,"date_created":"2019-10-23T09:54:43Z","file_id":"6962","creator":"cparanjape","file_name":"Chaitanya_Paranjape_source_files_tex_figures.zip","relation":"source_file","access_level":"closed"},{"access_level":"open_access","relation":"main_file","creator":"cparanjape","file_name":"Chaitanya_Paranjape_Thesis.pdf","date_created":"2019-10-23T10:37:09Z","file_id":"6963","file_size":19504197,"checksum":"642697618314e31ac31392da7909c2d9","content_type":"application/pdf","date_updated":"2020-07-14T12:47:46Z"}],"publication_identifier":{"eissn":["2663-337X"]},"oa":1,"alternative_title":["ISTA Thesis"],"doi":"10.15479/AT:ISTA:6957","OA_place":"publisher","ddc":["532"],"article_processing_charge":"No","citation":{"mla":"Paranjape, Chaitanya S. <i>Onset of Turbulence in Plane Poiseuille Flow</i>. Institute of Science and Technology Austria, 2019, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:6957\">10.15479/AT:ISTA:6957</a>.","short":"C.S. Paranjape, Onset of Turbulence in Plane Poiseuille Flow, Institute of Science and Technology Austria, 2019.","ieee":"C. S. Paranjape, “Onset of turbulence in plane Poiseuille flow,” Institute of Science and Technology Austria, 2019.","apa":"Paranjape, C. S. (2019). <i>Onset of turbulence in plane Poiseuille flow</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:6957\">https://doi.org/10.15479/AT:ISTA:6957</a>","ama":"Paranjape CS. Onset of turbulence in plane Poiseuille flow. 2019. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:6957\">10.15479/AT:ISTA:6957</a>","ista":"Paranjape CS. 2019. Onset of turbulence in plane Poiseuille flow. Institute of Science and Technology Austria.","chicago":"Paranjape, Chaitanya S. “Onset of Turbulence in Plane Poiseuille Flow.” Institute of Science and Technology Austria, 2019. <a href=\"https://doi.org/10.15479/AT:ISTA:6957\">https://doi.org/10.15479/AT:ISTA:6957</a>."},"_id":"6957","month":"10","title":"Onset of turbulence in plane Poiseuille flow","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","page":"138","has_accepted_license":"1","date_published":"2019-10-24T00:00:00Z","date_updated":"2026-04-08T07:46:58Z","year":"2019","oa_version":"Published Version","publisher":"Institute of Science and Technology Austria","type":"dissertation","day":"24","status":"public"}]