Slow-growth approximation for near-wall patch representation of wall-bounded turbulence

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. Strong pressure gradients,

however, complicate this characterization and 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 flow growth 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 gradient boundary layers indicate the asymptotic model successfully

accounts for the effect of boundary layer growth on the small-scale near-wall turbulence, even in the absence of

large-scale structures.