Plane Couette - symmetries

Turbulence within the S-invariant subspace

This movie illustrates the turbulent motion observed within the S-invariant subspace of the HKW cell.

Time interval from 0 to 200

The initial condition is a field from the , translated streamwise, spanwise to optimize the s₁, s₂ symmetries (to within 2% in the energy norm), and then projected to lie exactly in the S-invariant subspace.

(2007-09-03, 3 MB)

What is surprising about such simulations is that -even though a typical initial state of a fluid has a zero likelihood of being within (or entering) the S-invariant subspace- the turbulent dynamics seems to stays close to the S-invariant subspace turbulence for all times.

This observation motivates what follows, a closer investigation of the geometry of the state-space flow and numerical searches for steady state or equilibrium solutions within the S-invariant subspace.