On the influence of outer large-scale structures on near-wall turbulence in channel flow

Abstract

DNS data for channel flow at Re τ = 1025 are used to analyse the interaction between large outer scales in the log-law region -referred to as super-streaks -and the small-scale, streaky, streamwisevelocity fluctuations in the viscosity-affected near-wall layer. The study is inspired by extensive experimental investigations by Mathis, Marusic and Hutchins, culminating in a predictive model that describes, in a supposedly universal manner, the "footprinting" and "modulating" effects of the outer structures on the small-scale near-wall motions. The approach used herein is based on the examination of joint PDFs for the small-scale fluctuations, conditioned on regions of large-scale footprints. The large and small scales are separated by means of the Huang-Hilbert empirical-mode decomposition, the validity of which is demonstrated by way of pre-multiplied energy spectra, correlation maps and energy profiles for both scales. Observations derived from the PDFs then form the basis of assessing the validity of the assumptions underlying the model. Although the present observations support some elements of the model, the results imply that modulation by negative and positive large-scale fluctuations differ greatly -an asymmetric response that is not compatible with the model. The study is thus extended to examining the validity of an alternative proposal, which is based on the assumption that a universal description of the small-scale response to the large-scale motions has to rely on the velocity fluctuations being scaled with the largescales-modified local friction velocity, rather than with the mean value. This proposal is partially supported by the present analysis. Finally, an alternative, new phenomenological model is proposed and examined.

Spectral analysis of near-wall turbulence in channel flow at Reτ=4200 with emphasis on the attached-eddy hypothesis

“…This rather unexpected result has motivated the isolation of these small scales from larger scales by means of a spatially two-dimensional version of the Empirical Mode Decomposition (EMD), previously used by Agostini & Leschziner [32][33][34] . The distinction between small and large scales is not precise, and it depends of the number of intrinsic modes (here 6) used for the separation process.…”

Predicting the response of small-scale near-wall turbulence to large-scale outer motions

“…The above designation "universal" requires an important qualification in the context of the work by Agostini and Leschziner, 29 as well as the present study. In model (1), u * is not merely implied to be a signal that is decoupled from the outer structures within any one particular flow, but it is held to be "universal" for any Reynolds number, with the Reynolds-number dependence of the signal u + effected by the links to the outer structures, via the terms containing α and β.…”

“…Figure 1 thus demonstrates-as do other results for joint (u − w) PDFs, given in Agostini and Leschziner 29 -that Equation (1) does not yield a universal signal, even for the single Reynolds number being considered. In Agostini and Leschziner, 29 the present authors provide a preliminary version of a phenomenological predictive approach that is an alternative to Equation (1), and which yields a distinctly better overlap between the two sets of contours given in Figure 1. In addition, the model is shown to also secure a nearly universal behaviour of the (u * − w * ) PDFs.…”

“…The nature and intensity of this interaction have been the subject of a substantial number of experimental studies undertaken since 2007, mainly by Marusic, Smits, and their collaborators (e.g., Hutchins and Marusic, 17 Mathis et al, 18,19 Marusic et al, 20,21 Hutchins et al, 22 Mathis et al, 23 Mathis et al, 24 and Smits et al 25 ). Notable computations-based studies, which exploit DNSand LES-derived data to analyze interactions between outer structures and the statistical properties of near-wall turbulence, are those of Jiménez,4,26 Chung and McKeon, 16 Schlatter and Örlü, 27 Bernardini and Pirrozoli, 28 Agostini and Leschziner, 29 and Lee and Moser. 30 The outer-inner interaction may be described by two principal features: unsteady convective shifts of the "quasi-frozen" small-scale structure-referred to as "footprinting"-and an unsteady attenuation/amplification of the intensity of the energy of the small-scale fluctuations-referred to as "modulation"-with the unsteadiness of both processes having length-and time-scales associated with the large-scale outer structures.…”

A new identification method in sampled quadrant analysis for wall-bounded turbulence

“…The PDF of unclassified uv/⟨uv⟩ was measured before by Willmarth and Lu 8 in a turbulent boundary layer, while the PDFs of classified and unclassified uv/⟨uv⟩ were investigated by Brodkey, Wallace, and Eckelmann 12 in a turbulent channel flow. The joint PDF of u − v was also reported before by Wallace and Brodkey, 13 Agostini and Leschziner, 22 Hwang et al 23 In the present work, we have also studied the joint PDF of u − v and premultiplied joint PDF of u − v and the PDF of classified and unclassified uv/⟨uv⟩. In Figure 3(a), we show the PDFs of unclassified uv/⟨uv⟩ at eight different wall-normal locations from C2000.…”