Unstable periodic orbits and heteroclinic connections in plane Couette flow

2008/10/10 by John Gibson, John F. Gibson, Gibson, John F. +3
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Geomagnetism and Paleomagnetism Studies #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.0810.1974

Short paper accompanying video submitted to the Gallery of Fluid Motion for the 2008 meeting of the APS Division of Fluid Dynamics

arxiv created 2008/10/10 · openalex publication_date 2008/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of wall-bounded rolls and streaks and provide a framework for understanding low-Reynolds turbulent shear flows as dynamical systems. We present fluid dynamics videos of plane Couette flow illustrating periodic orbits, a close pass of turbulent flow to a periodic orbit, and heteroclinic connections between unstable equilibria.

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