article published yes Chaitanya S Paranjape author 3D85B7C4-F248-11E8-B48F-1D18A9856A87 Gökhan Yalniz author 66E74FA2-D8BF-11E9-8249-8DE2E56974250000-0002-8490-9312 Yohann Duguet author Nazmi B Budanur author 3EA1010E-F248-11E8-B48F-1D18A9856A870000-0003-0423-5010 Björn Hof author 3A374330-F248-11E8-B48F-1D18A9856A870000-0003-2057-2754 GradSch department BjHo department Revisiting the Turbulence Problem Using Statistical Mechanics project 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. American Physical Society2023 eng General Physics and Astronomy 0031-9007 1079-7114 2306.05098 37540883 00105292990000410.1103/physrevlett.131.034002 1313 https://research-explorer.ista.ac.at/record/19684 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. 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>. 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> 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> 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>. C.S. Paranjape, G. Yalniz, Y. Duguet, N.B. Budanur, B. Hof, Physical Review Letters 131 (2023). 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. 132742023-07-24T09:43:59Z2026-04-07T11:47:05Z