Dual views of periodic orbits and transient turbulenceEquilibria are stationary, no turbulence takes place there. The following dual-view movies show that the time dependence of typical unstable structures seen in turbulence is better captured by unstable periodic orbits. |
| T=35.77 periodic orbit: | T=97.08 periodic orbit |
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The period T=97.08 orbit (purple line) is a periodic orbit close to a two-period repeat of the period 35.77 orbit (dotted line); it is the beginning of the infinite hierarchy of unstable periodic orbits embedded in the turbulent flow.
From the 3D video it would be hard to tell that these are not segments of a typical turbulent orbit - unstable periodic orbits capture well the coherent structures observed in earlier videos.