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.
Physical Review Letters
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.).
Paranjape CS, Yalniz G, Duguet Y, Budanur NB, Hof B. Direct path from turbulence to time-periodic solutions. Physical Review Letters. 2023;131(3). doi:10.1103/physrevlett.131.034002
Paranjape, C. S., Yalniz, G., Duguet, Y., Budanur, N. B., & Hof, B. (2023). Direct path from turbulence to time-periodic solutions. Physical Review Letters. American Physical Society. https://doi.org/10.1103/physrevlett.131.034002
Paranjape, Chaitanya S, Gökhan Yalniz, Yohann Duguet, Nazmi B Budanur, and Björn Hof. “Direct Path from Turbulence to Time-Periodic Solutions.” Physical Review Letters. American Physical Society, 2023. https://doi.org/10.1103/physrevlett.131.034002.
C. S. Paranjape, G. Yalniz, Y. Duguet, N. B. Budanur, and B. Hof, “Direct path from turbulence to time-periodic solutions,” Physical Review Letters, vol. 131, no. 3. American Physical Society, 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.
Paranjape, Chaitanya S., et al. “Direct Path from Turbulence to Time-Periodic Solutions.” Physical Review Letters, vol. 131, no. 3, 034002, American Physical Society, 2023, doi:10.1103/physrevlett.131.034002.