Augmented Restricted Nonlinear (ARNL) Model for High Reynolds Number Wall-Turbulence

A restricted nonlinear (RNL) representation of wall-bounded turbulence accurately predicts key characteristics of low to moderate Reynolds number flows. This model limits nonlinear interactions to those producing streamwise constant dynamics (defined as large-scales), and restricts streamwise varying small-scales to lie within the region associated with peak outer-layer dissipation. Here, we propose an augmented RNL (ARNL) model that includes additional scales, but maintains order reduction by combining the large-scale dynamical restriction imposed in generalized quasilinear models with RNL band-limiting of the small-scales. This ARNL model with a single nonlinearly interacting streamwise varying mode is shown to yield more accurate predictions of low-order statistics versus the RNL model at \(\text {Re}_\tau =550\) and 1000. At \(\text {Re}_\tau = 2000\) , a second non-zero large-scale mode improves the fidelity of ARNL predictions.