Generalized quasi-linear simulation of plane Poiseuille flow

Quasi-linear (QL) simulations of shear-driven turbulence have gained popularity in recent years. Under the QL approximation, each flow field is decomposed into a suitable (e.g. streamwise) mean plus fluctuation component, and fluctuation/fluctuation nonlinearities are retained only where they feed back upon the mean fields. Marston et al. (Phys. Rev. Lett., 116, 2016) introduced the generalized quasi-linear (GQL) approximation to improve the accuracy of QL simulations relative to full direction numerical simulations (DNS). The GQL reduction is achieved by separating the flow variables into low and high modes via a spectral filter rather than by decomposition into a strict mean and fluctuations. Nonlinear coupling among the high modes is retained only where this coupling projects onto the dynamics of the low modes, which are allowed to undergo fully nonlinear interactions. Here, the accuracy and efficiency of GQL simulations of turbulent channel flow are evaluated relative to DNS and to QL simulations. Remarkably, retention of only a few low GQL modes is shown to increase accuracy dramatically. To increase computational efficiency, sideband truncations, in which only a localized band of high modes is retained, are explored.