Recent experimental and computational studies have demonstrated that wall-bounded turbulent shear flows exhibit universal small-scale dynamics that are modulated by large-scale flow structures. This characterization can be complicated, however, by stronger pressure gradients; 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 valid whenever the viscous length scale is small relative to the length scale over which the mean flow varies. The asymptotics inform a model for the effect of mean flowgrowth on near-wall turbulence in a small domain localized to the boundary whose size scales in viscous units. 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 wall-resolved large eddy simulation of adverse pressure gradientboundary layers indicate the asymptotic model successfully accounts for the effect of boundary layer growth on the small-scale near-wall turbulence.
