3a. Turbulence within the S-invariant subspace

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

[MOVIE] Time interval from 0 to 200.

The initial condition is a field from the previous simulation, 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 likelyhood 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 within the S-invariant subspace. This motivates numerical searches for steady state or equilibrium solution.