  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.
