Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

Abstract

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows

“…More qualitatively, we comment that the UMZ/VF flow structure analysed here may constitute a 'straight' section of a longer superstructure that slowly meanders in the streamwise direction, and that the coupling mechanisms elucidated herein have the potential both to complement those described by the modelling framework of Sharma et al [35] and to connect to the features observed in the numerical and physical experiments of Cossu & Hwang [36] and Baars et al [37], respectively. In contrast to the recent work by Hwang et al [11,12,16] discussed in §1, this study captures only a single interacting UMZ/VF 'unit'.…”

Logarithmic-layer turbulence: A view from the wall

“…Although the spectral expression of the reconstruction operator discussed in the previous section is very useful in understanding the behaviour of the different flow scales, its physical-space counterpart defined in (8) and (9) gives a more intuitive representation of the operation that is actually being performed. It is probably also easier to generalise to wall-bounded flows besides the channel.…”

“…This paper focuses on the properties of the estimations of logarithmic-layer turbulence using noiseless, although potentially incomplete, wall measurements from DNS. The widespread availability of data in the last years has allowed various research groups to test the performance of similar methods with considerable success [7][8][9][10][11]. These works differ from ours in that most of them focus on the use of physically motivated linear models [9,10] to relate velocity measurements at one y to predict the same velocity component at another wall-normal distance.…”

Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and

“…It is instructive to present an energy spectrogram: premultiplied spectra at 40 logarithmically-spaced positions within the range 10.6 z + δ + are presented with iso-contours of k + x φ + uu in Figure 1(a). These spectra were obtained from hot-wire measurements at Re τ ≈ 14 100 in Melbourne's TBL facility (Baars et al 2017a). Near-wall streaks (Kline et al 1967) dominate the inner-spectral peak in the TBL spectrogram (identified with the × marker at λ + x = 10 3 and z + = 15), while large-scale organized motions cause a broad spectral peak in the log-region, indicated with a × marker at λ x = 4δ and z + = 3.9Re 1 /2 τ ≈ 464 (Mathis et al 2009).…”