(296d) Spatially Invariant K-Means Clustering for Analyzing the Turbulent Attractor of Minimal Channel Flow

We describe a method for segregating the turbulent attractor into dynamically relevant regions using a spatially invariant K-means clustering method. Direct numerical simulations of turbulent plane Poiseuille flow at transitional Reynolds numbers are performed for minimal flow unit boxes, where exact traveling wave solutions of the Navier-Stokes equations, called Exact Coherent States (ECS), are known to dictate the dynamics. These ECS can be viewed as signals, so spatially invariant K-means clustering is first shown to capture simple traveling wave signals. Clustering the turbulent attractor with this method is then shown to segregate the state space and capture infrequent low drag (hibernating) events. Furthermore, the resulting clusters highlight the ubiquity of quasi-streamwise vortices in the turbulent attractor, and connections are drawn between the clusters and ECS.