Time evolution of turbulent Taylor-Couette flow is robustly captured by Exact Coherent Structures

Recent work has demonstrated that the time evolution of turbulent flows can be captured by simple, recurrent solutions of the Navier-Stokes equations called Exact Coherent Structures (ECSs). It is often assumed that an ECS quantitatively describes turbulence during an interval of time when turbulence is close (in state space) to the given ECS. In this talk, we present evidence suggesting that the dynamics of turbulence can be captured by ECSs with non-trivial temporal behavior even in cases where turbulence is not particularly close to an ECS. We have investigated numerous examples of turbulence co-evolving with (`shadowing') an ECS in a small-aspect-ratio Taylor-Couette flow. In this system, we have established a protocol for identifying intervals of time when turbulence shadows an ECS. We also discuss the difference in shadowing criteria for numerics and experiment.