Direct path from turbulence to time-periodic solutions
Abstract
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.
Cite
@article{arxiv.2306.05098,
title = {Direct path from turbulence to time-periodic solutions},
author = {Chaitanya S. Paranjape and Gökhan Yalnız and Yohann Duguet and Nazmi Burak Budanur and Björn Hof},
journal= {arXiv preprint arXiv:2306.05098},
year = {2023}
}
Comments
To be published in Physical Review Letters. 5 pages with 4 figures + supplemental material with 6 figures