Dual view of state space / 3D physical space dynamics

shows a plane Couette velocity field starting out close to NB equilibrium and evolving under Navier-Stokes on the right and the corresponding state-space trajectory on the left.
[state space / velocity field movie of plane couette flow]
The cell size, Reynolds number: [Lx, Ly, Lz] = [5.51, 2, 2.51] , Re=400. Grid size,time step: 32 x 49 x 32, dt = 0.03125. The fields in this section are within the S-invariant subspace.

The state-space projection is from the 105 dimensional state space onto a 2d plane (e1,e2) formed from linear combinations of the upper-branch equilibrium and its half-cell translations.

Keep the movie running: the accompagning narrative is provided in the next slide.

eqbaStatesp.html transient.html