Plane Couette - dual views

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

LM	Laminar equilibrium
LB UB	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.