This is an old revision of the document!
Let us see how this format works. For now I will just start writing. I hope that greater flexibility in the structure (multiple pages and links) will make it easy to reorganize as the material gathers.
I have been dissatisfied for quite a while with the projection basis sets I've used for plotting periodic orbits in the HKW cell. We don't have good equilibria there, so we can't easily do the translational-basis set we used for the narrow cell in the JFM08 paper. I have previously used a POD basis from the data of a single periodic orbit (P87p89). The plots were good, in that they showed turbulent trajectories lying in the same regions of state space as the periodic orbits, and forming similar pretty-well-defined shapes in whatever projection we looked at. But Predrag never liked this since it involved POD and averages, and to me, it was rhetorically weak to use a basis based on periodic orbits to argue that the periodic orbits live where turbulence is.
So, I decided to compare the orbit-POD basis to a translational basis based on a single velocity field (for Predrag) and a turbulent-data POD basis (for me). It turns out they're all remarkably similar.
Some key points:
* The turbulent POD basis was constructed from about two hundred samples over a trajectory of several thousand time units. The basis clearly reflects the fixed z-phase of the roll-streak structures.