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

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160077 ◽  
Author(s):  
W. J. Baars ◽  
N. Hutchins ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Wall Turbulence ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Scale Interaction ◽  
High Reynolds ◽  
Near Wall

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’.

scholarly journals Large-scale influences in near-wall turbulence

2007 ◽  
Vol 365 (1852) ◽  
pp. 647-664 ◽  
Author(s):  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Scale Separation ◽  
Large Scale Motion ◽  
High Reynolds ◽  
Scale Motion ◽  
Near Wall Turbulence ◽  
Near Wall

Hot-wire data acquired in a high Reynolds number facility are used to illustrate the need for adequate scale separation when considering the coherent structure in wall-bounded turbulence. It is found that a large-scale motion in the log region becomes increasingly comparable in energy to the near-wall cycle as the Reynolds number increases. Through decomposition of fluctuating velocity signals, it is shown that this large-scale motion has a distinct modulating influence on the small-scale energy (akin to amplitude modulation). Reassessment of DNS data, in light of these results, shows similar trends, with the rate and intensity of production due to the near-wall cycle subject to a modulating influence from the largest-scale motions.

scholarly journals Turbulent plane Couette flow at moderately high Reynolds number

2014 ◽  
Vol 751 ◽  
Author(s):  
V. Avsarkisov ◽  
S. Hoyas ◽  
M. Oberlack ◽  
J. P. García-Galache
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Wall Layer ◽  
Wall Region ◽  
Plane Couette Flow ◽  
Turbulent Plane ◽  
High Reynolds ◽  
Near Wall

AbstractA new set of numerical simulations of turbulent plane Couette flow in a large box of dimension ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}20\pi h,\, 2h,\, 6\pi h$) at Reynolds number $(\mathit{Re}_{\tau }) =125$, 180, 250 and 550 is described and compared with simulations at lower Reynolds numbers, Poiseuille flows and experiments. The simulations present a logarithmic near-wall layer and are used to verify and revise previously known results. It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. On the contrary, the wall-normal intensity scales in inner units in the near-wall region and in outer units in the core region. The spectral ridge found by Hoyas & Jiménez (Phys. Fluids, vol. 18, 2003, 011702) for the turbulent Poiseuille flow can also be seen in the present flow. Away from the wall, very large-scale motions are found spanning through all the length of the channel. The statistics of these simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

scholarly journals Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

2009 ◽  
Vol 628 ◽  
pp. 311-337 ◽  
Author(s):  
ROMAIN MATHIS ◽  
NICHOLAS HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Supporting Evidence ◽  
Scale Structures ◽  
Small Scale Structures ◽  
Near Wall

In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

scholarly journals Extreme dissipation and intermittency in turbulence at very high Reynolds numbers

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200591
Author(s):  
Gerrit E. Elsinga ◽  
Takashi Ishihara ◽  
Julian C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Small Scale ◽  
Scaling Exponent ◽  
High Reynolds Numbers ◽  
Layer Structures ◽  
High Reynolds ◽  
Very High

Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

scholarly journals Wall-attached structures of velocity fluctuations in a turbulent boundary layer

2018 ◽  
Vol 856 ◽  
pp. 958-983 ◽  
Author(s):  
Jinyul Hwang ◽  
Hyung Jin Sung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Wall Turbulence ◽  
Velocity Fluctuations ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Logarithmic Region ◽  
High Reynolds ◽  
Attached Eddies

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Study of turbulent structure with hot wires smaller than the viscous length

1984 ◽  
Vol 142 ◽  
pp. 121-149 ◽  
Author(s):  
William W. Willmarth ◽  
Lalit K. Sharma
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Gradient ◽  
Shear Layers ◽  
Small Scale ◽  
Wall Region ◽  
Burst Frequency ◽  
Velocity Fluctuations ◽  
Hot Wires ◽  
Scale Shear

The small-scale structure of the streamwise velocity fluctuations in the wall region of a turbulent boundary layer is examined in a new wind-tunnel facility using hot-wires smaller than any previously constructed (typical dimensions: l = 25 μm, d = 0.5 μm). In the boundary layer in which the measurements were made, the ratio of the hot-wire length to the viscous length is 0.3. The turbulent intensity measured with the small hot wires is larger than that measured with longer wires owing to the better spatial resolution of the small wires. The velocity fluctuations measured by the small hot wires are also analysed to determine the burst frequency at two Reynolds numbers and at various distances from the wall. The dimensionless burst frequency does not depend on the Reynolds number when scaled with wall parameters. However, it increases with Reynolds number when scaled with outer variables. Velocity fluctuations measured by two hot wires, less than two viscous lengths apart, are analysed to reveal the small-scale features present during a burst and in the absence of a burst. The main conclusions are: (1) intermittent small-scale shear layers occur most frequently when bursts are present, less frequently just after a burst, and even less frequently just before a burst; and (2) on occasion the velocity gradient of the small-scale shear layers is as large as the mean-velocity gradient at the wall.

Hot-wire spatial resolution issues in wall-bounded turbulence

2009 ◽  
Vol 635 ◽  
pp. 103-136 ◽  
Author(s):  
N. HUTCHINS ◽  
T. B. NICKELS ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Spatial Resolution ◽  
Reynolds Numbers ◽  
Energy Spectra ◽  
Small Scale ◽  
Wire Length ◽  
Hot Wire ◽  
Wide Range ◽  
Near Wall

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

Sign in / Sign up

Export Citation Format

Share Document