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

Abstract

Self-similarity of wall-attached coherent structures in a turbulent channel at $R{e}_{\tau }=543$ 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 (Borée, 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-Durán, 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.

arXiv comment30 pages, 18 figures

References in corpus (21)

• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• A critical layer model for turbulent pipe flow
• Spectral analysis of jet turbulence
• On a self-sustained process at large scale in the turbulent channel flow
• The lift-up effect: the linear mechanism behind transition and turbulence in shear flows
• Model-based scaling of the streamwise energy density in high-Reynolds number turbulent channels
• Color of turbulence
• Resolvent-based modelling of coherent wavepackets in a turbulent jet
• Resolvent-based estimation of space-time flow statistics
• On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows
• SPOD and resolvent analysis of near-wall coherent structures in turbulent pipe flows
• The colour of forcing statistics in resolvent analyses of turbulent channel flows
• Energy transfer in turbulent channel flows and implications for resolvent modelling
• Two-dimensional energy spectra in high Reynolds number turbulent boundary layers
• Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow
• Resolvent-based estimation of turbulent channel flow using wall measurements
• Ambiguity in mean-flow-based linear analysis
• Statistical behaviour of self-similar structures in canonical wall turbulence
• A spectral-scaling based extension to the attached eddy model of wall-turbulence
• Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence
• Accurate Frequency Domain Identification of ODEs with Arbitrary Signals

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