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The majority of practical flows, particularly those flows in applications ofimportance to transport, distribution and climate, are turbulent and as aresult experience complex three-dimensional motion with increased drag comparedwith the smoother, laminar condition. In this study, we describe thedevelopment of a simple model that predicts important structural and scalingfeatures of wall turbulence. We show that a simple linear superposition ofmodes derived from a forcing-response analysis of the Navier-Stokes equationscan be used to reconcile certain key statistical and structural descriptions ofwall turbulence. The computationally cheap approach explains and predictsvortical structures and velocity statistics of turbulent flows that havepreviously been identified only in experiments or by direct numericalsimulation. In particular, we propose an economical explanation for themeandering appearance of very large scale motions observed in turbulent pipeflow, and likewise demonstrate that hairpin vortices are predicted by themodel. This new capability has clear implications for modeling, simulation andcontrol of a ubiquitous class of wall flows.

Predicting structural and statistical features of wall turbulence