Abstract:  In near-wall regions, turbulent flow is dominated by a few energetic structures. Aubry, Holmes, Lumley, and Stone (JFM 192, 1988) used proper orthogonal decomposition and Galerkin projection to develop low-dimensional dynamical systems models of coherent structures in the turbulent boundary layer. We examine Aubry et al.'s derivation in order to understand the models' lack of predictive accuracy (specifically, the treatment of boundary conditions, mean flow, and unresolved modes) and reformulate the problem for the more tractable case of plane Couette flow. Here we find that model accuracy is limited by the slow convergence of Galerkin projection and eddy-viscosity modeling. Yet numerical simulations show that the flow's evolution is largely determined by moderately low-dimensional states, suggesting that accurate dynamical systems models are possible, in principle.