The role of exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow*

The interpretation of fluid turbulence as a deterministic walk between neighborhoods of unstable nonchaotic solutions of the Navier-Stokes equation (known as exact coherent structures, ECS) has offered a new perspective on the physical mechanisms that sustain the turbulent dynamics and control the transition from laminar flow. In particular, we have demonstrated that ECS in weakly turbulent Taylor-Couette flow can be found using a combination of recurrence analysis and parameter continuation. The relative periodic orbits and relative equilibria that we computed were shown to play a dynamically important role. In particular, their neighborhoods are visited closely and frequently by the turbulent flow. Furthermore, saddle-node bifurcations at which some of these solutions (dis)appear correspond quite precisely to qualitative changes in turbulent dynamics and/or relaminarization of the flow.