Within the last few years the dynamical (as opposed to statistical) theory of moderate Re boundary shear turbulence has made great strides; the geometry of the infinite-dimensional Navier-Stokes state space (not low-dimensional models) can now be triangulated by sets of exact solutions (equilibria, traveling waves, periodic orbits, ...). They, together with their stable/unstable manifolds and the heteroclinic connections between various exact solutions, form a rigid backbone which enables us to describe, control and predict the sinuous motions of a turbulent fluid.
The following dual-view movie shows that the time evolution of typical unstable structures observed in turbulence is better captured by unstable periodic orbits embedded in the turbulent regions of the state space.
(if flash does not play: mp4 format, 1.3 MB)
The states-space visualization is novel, and might be of interest even for an expert fluid dynamicst. The tutorial develops the theory behind this movie in a sequence of gentle steps.