Using exact coherent structures to describe intermittent Taylor-Couette flow

A dynamical systems approach to understanding turbulence suggests that the complicated motion of turbulent flow is shaped by special solutions of the Navier-Stokes equations known as exact coherent structures (ECSs). In this picture, turbulent flow co-evolves with, or "shadows", at least one such solution for a time; then a different ECS; and so on. Here we describe how ECSs can characterize flow in a Taylor-Couette experiment exhibiting temporal intermittency with periods of high regularity (quiescence) alternating with time intervals of significant spatial and temporal irregularity (activity). A collection of ECSs is found that describes this behavior for almost the entire duration of the flow, in both experimental and numerical investigations, for both quiescent and active periods of the flow. It is also demonstrated that the transition between quiescence and activity is mediated by a specific ECS that connects both regions. Finally, observables of the flow are shown to be well-represented by weighted averages of ECS observables, thereby demonstrating the connection between dynamical shadowing of ECSs and average observables in a 3-dimensional experimental flow.