  Non-equilibrium wall turbulence with mean-flow three-dimensionality is
ubiquitous in geophysical and engineering flows. Under these conditions,
turbulence may experience a counter-intuitive depletion of the turbulent
stresses, which has important implications for modelling and control. Yet,
current turbulence theories have been established mainly for statistically
two-dimensional equilibrium flows and are unable to predict the reduction in
the Reynolds stress magnitude. In the present work, we propose a multiscale
model which explains the response of non-equilibrium wall-bounded turbulence
under the imposition of three-dimensional strain. The analysis is performed via
direct numerical simulation of transient three-dimensional turbulent channels
subjected to a sudden lateral pressure gradient at friction Reynolds numbers up
to 1,000. We show that the flow regimes and scaling properties of the Reynolds
stress are consistent with a model comprising momentum-carrying eddies with
sizes and time scales proportional to their distance to the wall. We further
demonstrate that the reduction in Reynolds stress follows a spatially and
temporally self-similar evolution caused by the relative horizontal
displacement between the core of the momentum-carrying eddies and the flow
layer underneath. Inspection of the flow energetics reveals that this mechanism
is associated with lower levels of pressure-strain correlation which ultimately
inhibits the generation of Reynolds stress. Finally, we assess the ability of
the state-of-the-art wall-modelled large-eddy simulation to predict
non-equilibrium, three-dimensional flows.
