Self-similar mechanisms in wall turbulence studied using of resolvent analysis

TL;DR

This study uses resolvent analysis to investigate the self-similarity of wall-attached coherent structures and their forcing in turbulent channel flow, confirming Townsend's hypothesis at a specific Reynolds number.

Contribution

It demonstrates the self-similarity of flow structures and forcing in wall turbulence using resolvent analysis and advanced decomposition techniques.

Findings

Wall-attached structures exhibit self-similarity consistent with Townsend's hypothesis.

Forcing structures also show self-similarity in certain components.

Quantitative agreement with theoretical predictions of self-similar attached eddies.

Abstract

Self-similarity of wall-attached coherent structures in a turbulent channel at $Re_\tau=543$ is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised, frequency-dependent Reynolds stresses, considered to act as an endogenous forcing. We assess the self-similarity of both the wall-attached flow structures and the associated forcing. The former are educed from direct numerical simulation data by finding the flow field correlated with the wall shear, whereas the latter is identified using a frequency space version of Extended Proper Orthogonal Decomposition (Bor\'{e}e, J. 2003 Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Experiments in fluids 35 (2), 188-192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne \emph{et al}. (Towne, A., Lozano-Dur\'{a}n, A. & Yang, X. 2020 Resolvent-based estimation of space-time flow statistics. Journal of Fluid Mechanics 883, A17). The analysis reveals self-similarity of both wall-attached structures$-$in quantitative agreement with Townsend's hypothesis of self-similar attached eddies$-$and the underlying forcing, at least in certain components.