Complete Matched Asymptotic Expansions for Velocity Statistics in Turbulent Channels

TL;DR

This paper develops high-fidelity matched asymptotic expansions for turbulence statistics in channel flow, validated by DNS data, revealing specific overlap forms for different stress components and analyzing velocity profile oscillations.

Contribution

It introduces a rigorous a priori test for overlap identification in MAE and provides the first MAE analysis of wall-normal stress <vv> in turbulent channel flow.

Findings

Supports the c0 - c1 Y^{1/4} overlap form for <uu> and <ww> stresses.

Discovers a c0 - c1 Y^{5/4} overlap form for <vv> stress.

Analyzes spatial oscillations of the mean velocity indicator function.

Abstract

Complete high fidelity matched asymptotic expansions (abbreviated MAE) are developed for the first and second order turbulence statistics in channel flow from 11 direct numerical simulations (DNS). To put the crucial identification of overlaps on a solid footing, a simple a priori test is devised, which only requires a DNS or experimental profile and the presumed overlap of the MAE for the quantity in question. This test fully supports the form c0 - c1 Y^1/4 of the overlaps for the stream-wise and cross-stream normal stresses <uu> and <ww>, which has been advocated by Chen and Sreenivasan (2022, 2023, 2025) and Monkewitz (2022, 2023). The first MAE analysis of the wall-normal stress <vv> then reveals an overlap of the form c0 - c1 Y^5/4 , which is extensively documented. Finally, the logarithmic indicator function Xi = y dU/dy for the mean velocity overlap is reanalyzed, with focus on its spatial oscillations. The latter are compared in the concluding section to the spatial oscillations of <uu>, together with further observations.