# On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

## TL;DR

This study demonstrates that including Reynolds stresses via eddy-viscosity in resolvent analysis significantly improves the estimation of turbulent coherent structures in wall-bounded flows, especially at buffer-layer scales.

## Contribution

It shows the importance of incorporating Reynolds stresses in resolvent models to accurately predict turbulent flow structures and spectra.

## Key findings

- Reynolds stresses improve resolvent spectral estimates.
- Eddy-viscosity inclusion enhances peak frequency and location predictions.
- Matching forcing spectra further improves model accuracy.

## Abstract

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at friction Reynolds number Re$_\tau$ = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associated to the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes.