Transition to turbulence: highway through the edge of chaos is charted by Koopman modes

We present evidence of low-dimensional dynamical state-space structures enabling transition to turbulence using an extension of the recently advanced operator-theoretic approach to turbulence of Mezić (2005). To do this, we use the dynamic-mode-decomposition (DMD) algorithm of Schmid & Sesterhenn (2008) on the minimal seed trajectories in plane Couette flow of Rabin et al. (2012) and Eaves & Caulfield (2015), which transition to turbulence via the most energy-efficient finite amplitude perturbation from the laminar state. The methodology enables identification of low dimensional structures associated with stable and unstable manifolds of exact solutions to the Navier-Stokes equations, even though the state space is very high-dimensional. In consequence, the results provide a low-dimensional representation of the transition to turbulence and also identify the first known dynamical signature of the importance of edge states in this transition.