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

TL;DR

This paper develops an asymptotic model to accurately represent near-wall turbulence in wall-bounded flows with strong pressure gradients, validated against numerical simulations.

Contribution

It introduces a novel asymptotic analysis-based model that accounts for mean flow growth effects on near-wall turbulence in a localized domain.

Findings

Model accurately predicts near-wall turbulence statistics.

Successfully captures effects of boundary layer growth.

Validated against DNS and LES data.

Abstract

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.