Simultaneous shadowing of multiple Exact Coherent Structures in experimental Taylor-Couette flow

Eberhard Hopf first envisioned turbulent flow as being comprised of a sequence of special solutions of the governing equations, often referred to as Exact Coherent Structures (ECS). In this picture, turbulent flow co-evolves with, or "shadows", one such solution for a time; then a different ECS; and so on. This qualitative picture has recently been confirmed quantitatively in experimental Taylor-Couette flow. We demonstrate that this three-dimensional turbulent flow shadows, episodically but repeatedly, the spatial and temporal structure of multiple ECSs. We also unexpectedly observe that more than one ECS may be shadowed simultaneously by the turbulent flow. We explain this phenomenon in part through the relation of certain ECSs via bifurcations, as well as the similarity of segments of unrelated ECSs.