  Wall-bounded turbulent shear flows are known to exhibit universal small-scale
dynamics that are modulated by large-scale flow structures. Strong pressure
gradients complicate this characterization, however; they can cause significant
variation of the mean flow in the streamwise direction. For such situations, we
perform asymptotic analysis of the Navier-Stokes equations to inform a model
for the effect of mean flow growth on near-wall turbulence in a small domain
localized to the boundary. The asymptotics are valid whenever the viscous
length scale is small relative to the length scale over which the mean flow
varies. To ensure the correct momentum environment, a dynamic procedure is
introduced that accounts for the additional sources of mean momentum flux
through the upper domain boundary arising from the asymptotic terms.
Comparisons of the model's low-order, single-point statistics with those from
direct numerical simulation and well-resolved large eddy simulation of
adverse-pressure gradient turbulent boundary layers indicate the asymptotic
model successfully accounts for the effect of boundary layer growth on the
small-scale near-wall turbulence.
