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Turbulence in the restricted nonlinear (RNL) dynamics is analyzed andcompared with DNS of Poiseuille turbulence at $R=1650$. The structures areobtained by POD analysis of the two components of the flow partition used inRNL dynamics: the streamwise-mean flow and fluctuations. POD analysis of thestreamwise-mean flow indicates that the dominant POD modes, in both DNS andRNL, are roll-streaks harmonic in the spanwise. However, we conclude that thesePOD modes do not occur in isolation but rather are Fourier components of acoherent roll-streak structure. POD analysis of the fluctuations in DNS and RNLreveals similar complex structures consisting in part of oblique wavescollocated with the streak. The origin of these structures is identified bytheir correspondence to POD modes predicted using a stochastic turbulence model(STM). These predicted POD modes are dominated by the optimally growingstructures on the streak, which the STM predicts correctly to be of sinuousoblique wave structure. This close correspondence between the roll-streakstructure and the associated fluctuations in DNS, RNL and the STM implies thatthe self-sustaining mechanism operating in DNS is essentially the same as thatin RNL, which has been previously associated with optimal perturbation growthon the streak.

POD-based study of turbulent plane Poiseuille flow: comparing structure and dynamics between quasi-linear simulations and DNS