Turbulence vs. periodic solutions

What is striking about the periodic solutions is how visually similar they are to the turbulent dynamics: they also capture episodes of highly ordered motion along streamwise counter-rotating rolls, interspersed by turbulent episodes.

This movie shows a time segment of typical sustained turbulence:


The initial condition is a random perturbation from laminar flow.

(2007-09-04, 15 MB)

Given only a segment of periodic orbit movie we would have no way of guessing that the dynamics is exactly periodic in time.

Now that we have many exact solutions of Navier-Stokes equations: how do we visualize them, fit them together?