Joint reduced model for the laminar and chaotic attractors in plane Couette flow

We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow restricted to the shift–reflect invariant subspace in the permanently chaotic regime at ${Re}=187.8$ studied by Kreilos & Eckhardt (2012, Chaos: Interdisciplinary J. Nonlinear Sci., vol. 22, 047505). Our three-dimensional model is obtained by restricting the dynamics to the slowest mixed-mode SSM of the edge state. We show that this results in a nonlinear model that accurately reconstructs individual trajectories, representing the entire chaotic attractor and the laminar dynamics simultaneously. In addition, we derive a two-dimensional Poincaré map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor.