Plane Couette -

Heteroclinic connections

Here we are, wandering in 61,506 dimensions. Can one slice up this high-dimensional state space into subregions, develop symbolic dynamics that describes these exact time-invariant solutions of Navier-Stokes equations?


Each heteroclinic connection (see `arXiv.org:0808.1865`) is traced out by an infinite-time state space trajectory, ie., it corresponds to one 3D flow evolving in time. Dual visualization helps develop intuition about how states of different arrangements of rolls and streaks transmogrify into each other partition state space into regions tied to each other by robust heteroclinic connections