Global state space visualization

This global portrait shows several equilibria of plane Couette flow, together with segments of their unstable manifolds traced by evolving the velocity field under Navier-Stokes.

[state space projection of plane Couette flow]

The labeled points are


Laminar equilibrium

lower/upper-branch equilibrium (Nagata, Waleffe)
NB "newbie" equilibrium (Gibson, Halcrow, Cvitanović)
u(t) time-varying velocity field, evolving under Navier-Stokes

The fields in this section of the tutorial are within the S-invariant subspace.

The state-space projection is from the 105 dimensional space of free variables in the CFD algorithm onto a 2d plane (e1,e2) formed from linear combinations of the upper-branch equilibrium and its half-cell translations, with the laminar equilibrium as the origin. halfcellshifts1.html thousPix.html