Exact Coherent Structures in turbulent small-aspect-ratio Taylor-Couette flow
Krygier, Michael C.
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Turbulent flows are ubiquitous, so understanding their nature and dynamics and the ability to make definitive predictions about their behavior is of tremendous practical importance. Substantial progress in this direction has been made recently using a dynamical systems approach that exploits unstable non-chaotic recurrent solutions of Navier-Stokes that are known as Exact Coherent Structures (ECSs). These solutions capture fundamental features of classical empirically observed coherent structures in turbulent flows and come in the form of equilibria or periodic orbits. Numerical and limited experimental evidence suggests that turbulence can be described as a deterministic walk between neighborhoods of ECSs, with the turbulent trajectory following the stable and unstable manifolds of these ECSs in a high-dimensional state space. This work focuses on exploring the relevance and usefulness in a practical setting of an ECS-based description of turbulent dynamics using direct numerical simulations (DNS) in Taylor-Couette flow. A systematic approach to finding dynamically relevant ECSs is presented. We show the ECSs that we have computed play a dynamically important role, as their neighborhoods are visited frequently by the turbulent flow. Furthermore, it is found that bifurcations at which some of these solutions (dis)appear correspond quite precisely to qualitative changes in the turbulent dynamics and/or relaminarization of the flow.