Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel

TL;DR

This study improves the restricted nonlinear (RNL) model for turbulent flow in a half-channel by limiting its streamwise modes, resulting in mean velocity profiles that align with the standard logarithmic law at higher Reynolds numbers.

Contribution

Introducing a band-limited RNL model that enhances the accuracy of mean velocity profiles in turbulent flow simulations at higher Reynolds numbers.

Findings

Band-limited RNL models produce standard logarithmic velocity profiles.

Limiting streamwise modes improves model predictions at high Re.

Standard logarithmic behavior observed at higher Reynolds numbers.

Abstract

Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a logarithmic region is observed, its von-K\'arm\'an constant is not consistent with the standard logarithmic law. In half-channel flow we show that limiting the streamwise-varying wavenumber support of RNL turbulence to one or few empirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNL model follow standard logarithmic behavior for the higher Reynolds numbers in this study.