A proper-orthogonal-decomposition–based model for the wall layer of a turbulent channel flow

In this paper we investigate a proper orthogonal decomposition (POD)-based model for the wall layer of a turbulent channel flow. The model is based on the original derivation of Aubry et al. [J. Fluid Mech. 192, 115 (1988)] and includes 220 independent modes with 11 modes in each horizontal direction and one wall-normal mode. We use direct numerical simulation to evaluate and calibrate the closure assumptions. The nature of the energy transfer to unresolved scales is examined in detail. The POD modes integrated from the model are compared to those directly computed from the simulation. The model is shown to be sensitive to initial conditions. Special attention is given to the zero streamwise subspace, which is characterized by chaotic solutions loosely related to a cluster of traveling waves. The statistics of the model are shown to be in relatively good agreement with the simulation, with a limited dependence on the calibration procedure.