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Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel,and plane Couette flows can now be computed precisely at Reynolds numbers abovethe onset of turbulence. These invariant solutions capture the complex dynamicsof wall-bounded rolls and streaks and provide a framework for understandinglow-Reynolds turbulent shear flows as dynamical systems. We present fluiddynamics videos of plane Couette flow illustrating periodic orbits, a closepass of turbulent flow to a periodic orbit, and heteroclinic connectionsbetween unstable equilibria.

Unstable periodic orbits and heteroclinic connections in plane Couette flow