  The majority of practical flows, particularly those flows in applications of
importance to transport, distribution and climate, are turbulent and as a
result experience complex three-dimensional motion with increased drag compared
with the smoother, laminar condition. In this study, we describe the
development of a simple model that predicts important structural and scaling
features of wall turbulence. We show that a simple linear superposition of
modes derived from a forcing-response analysis of the Navier-Stokes equations
can be used to reconcile certain key statistical and structural descriptions of
wall turbulence. The computationally cheap approach explains and predicts
vortical structures and velocity statistics of turbulent flows that have
previously been identified only in experiments or by direct numerical
simulation. In particular, we propose an economical explanation for the
meandering appearance of very large scale motions observed in turbulent pipe
flow, and likewise demonstrate that hairpin vortices are predicted by the
model. This new capability has clear implications for modeling, simulation and
control of a ubiquitous class of wall flows.
