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.

 

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