Multi-scale periodic orbits in plane Couette flow: a reduced-order model perspective

Plane Couette flow at Re = 1200 is investigated in the minimal multi-scale flow unit (i.e. a flow unit with only two spanwise integral length scales), a system for which the computation of invariant solutions that are physically representative of the turbulent state has been understood to be challenging. To address this challenge, we employ an accurate reduced-order model (ROM) with 600 degrees of freedom (Cavalieri & Nogueira, Phys. Rev. Fluids, vol. 7, 2022, L102601). Invariant solutions of the ROM are computed, including 96 equilibria and 43 periodic orbits. The computed equilibrium solutions are found to be unable to fully reproduce sound energy balance associated with the multi-scale dynamics of the turbulent state. Periodic orbits are found to provide a more sensible description for multi-scale turbulent dynamics and the related energetics, as such invariant solutions with a sufficiently long period retain the complex spatiotemporal dynamics associated with the known multi-scale phenomena.