Energy or L2 norm

The kinetic energy of the fluid  E = (u,u)/2  endows the vectors in state space (velocity field across entire cell at a given instant in time) with a physically motivated bilinear form, a vector dot product:

Enorm

THE IDEA: pick a few fluid states frequently visited by the turbulent flow, and visualize the infinite-dimensional flow by projecting it onto coordinate frames constructed from such states.