Self-similar mechanisms in wall turbulence, through the lens of resolvent analysis

U. Karban, E. Martini, A. V. G. Cavalieri, L. Lesshafft, P. Jordan

Published 2021-05-27Version 1

Self-similarity of coherent structures in turbulent channels 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 external forcing. We assess the self-similarity of both the flow structures and the associated forcing. The former are educed from direct numerical simulation data using Spectral Proper Orthogonal Decomposition, whereas the latter are 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 et al. (2020) (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 coherent structures$-$supporting Townsend's notion of attached eddies$-$and the underlying forcing, and it is observed for simulations in which $Re_\tau$ varies from 180 to 1000, indicating self-similar dynamics over a broad range of turbulent scales.