What these movies illustrate

There are three kinds of animations here:

3D movies of velocity fields
turbulent flows visiting unstable coherent structures
State-space trajectories, which show
  1. that coherent structures result from close passes to unstable equilibrium solutions of Navier-Stokes, and
  2. that the equilibria and their unstable manifolds impart a rigid structure to state space that organizes the turbulent dynamics.
Dual views
shows some of these animations side-by-side. In these, you will see recurrent coherent structures appear in the turbulent velocity field as the state-space trajectory makes close passes to equilibrium solutions of Navier-Stokes.

In what follows, the key ideas are illustrated in the context of plane Couette flow. Similar phenomena have been observed in pipe flows.

Question: “ I am [ experimentalist | fluid dynamics theorist | engineer | cardiologist/biomedical engineer | quantum field theorist | computer scientist | weatherwoman ]. Should I have a look at this tutorial?”
Comment: “I am a turbulence expert. This is not turbulence.