scholarly journals Mathematical model for logarithmic scaling of velocity fluctuations in wall turbulence

2015 ◽  
Vol 92 (6) ◽  
Author(s):  
Hideaki Mouri
Keyword(s):  
Mathematical Model ◽  
Wall Turbulence ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling

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.

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 Velocity and spatial distribution of inertial particles in a turbulent channel flow

2019 ◽  
Vol 872 ◽  
pp. 367-406 ◽  
Author(s):  
Kee Onn Fong ◽  
Omid Amili ◽  
Filippo Coletti
Keyword(s):  
Spatial Distribution ◽  
Particle Velocity ◽  
Turbulent Channel Flow ◽  
Wall Turbulence ◽  
Buffer Layers ◽  
Working Fluid ◽  
Wall Region ◽  
Inertial Particles ◽  
Velocity Fluctuations ◽  
Near Wall

We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in turbulent downward flow through a vertical channel at friction Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=235$ and 335. The working fluid is air laden with size-selected glass microspheres, having Stokes numbers $St=\mathit{O}(10)$ and $\mathit{O}(100)$ when based on the Kolmogorov and viscous time scales, respectively. Cases at solid volume fractions $\unicode[STIX]{x1D719}_{v}=3\times 10^{-6}$ and $5\times 10^{-5}$ are considered. In the more dilute regime, the particle concentration profile shows near-wall and centreline maxima compatible with a turbophoretic drift down the gradient of turbulence intensity; the particles travel at speed similar to that of the unladen flow except in the near-wall region; and their velocity fluctuations generally follow the unladen flow level over the channel core, exceeding it in the near-wall region. The denser regime presents substantial differences in all measured statistics: the near-wall concentration peak is much more pronounced, while the centreline maximum is absent; the mean particle velocity decreases over the logarithmic and buffer layers; and particle velocity fluctuations and deposition velocities are enhanced. An analysis of the spatial distributions of particle positions and velocities reveals different behaviours in the core and near-wall regions. In the channel core, dense clusters form which are somewhat elongated, tend to be preferentially aligned with the vertical/streamwise direction and travel faster than the less concentrated particles. In the near-wall region, the particles arrange in highly elongated streaks associated with negative streamwise velocity fluctuations, several channel heights in length and spaced by $\mathit{O}(100)$ wall units, supporting the view that these are coupled to fluid low-speed streaks typical of wall turbulence. The particle velocity fields contain a significant component of random uncorrelated motion, more prominent for higher $St$ and in the near-wall region.

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’.

Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence

2012 ◽  
Vol 24 (3) ◽  
pp. 035110 ◽  
Author(s):  
Peter Lenaers ◽  
Qiang Li ◽  
Geert Brethouwer ◽  
Philipp Schlatter ◽  
Ramis Örlü
Keyword(s):  
Wall Turbulence ◽  
Normal Velocity ◽  
Velocity Fluctuations ◽  
Near Wall Turbulence ◽  
Near Wall

Scaling of second- and higher-order structure functions in turbulent boundary layers

2015 ◽  
Vol 769 ◽  
pp. 654-686 ◽  
Author(s):  
C. M. de Silva ◽  
I. Marusic ◽  
J. D. Woodcock ◽  
C. Meneveau
Keyword(s):  
Large Scale ◽  
Scaling Laws ◽  
Strong Support ◽  
Structure Functions ◽  
Higher Order ◽  
Wall Turbulence ◽  
Inertial Subrange ◽  
Order Structure ◽  
Logarithmic Scaling ◽  
Logarithmic Region

The statistical properties of wall turbulence in the logarithmic region are investigated using structure functions of the streamwise velocity. To this end, datasets that span several orders of magnitude of Reynolds numbers are used, up to$Re_{{\it\tau}}=O(10^{6})$, providing uniquely large scale separations for scrutinising previously proposed scaling laws. For the second-order structure functions strong support is found simultaneously for power-law scalings in the Kolmogorov inertial subrange and for logarithmic scaling at larger scales within the inertial range ($z<r\ll {\it\delta}$, where$z$is the distance from the wall,$r$the scale, and${\it\delta}$the boundary layer thickness). The observed scalings are shown to agree between the datasets, which include both temporal and spatial velocity signals and span from laboratory to atmospheric flows, showing a degree of universality in the results presented. An examination of higher even-order structure functions also shows support for logarithmic scaling behaviour for$z<r\ll {\it\delta}$, provided that the Reynolds number is sufficiently high. These findings are interpreted by generalising the work of Meneveau & Marusic (J. Fluid Mech., vol. 719, 2013) and introducing bridging relations between higher-order moments of velocity fluctuations and structure functions. Further, a physical model based on the attached-eddy hypothesis is utilised to derive various properties of the structure functions for the energy-containing scales of the logarithmic region. The descriptions derived from the model are shown to be supported by the experimental data.

scholarly journals Two-point correlation in wall turbulence according to the attached-eddy hypothesis

2017 ◽  
Vol 821 ◽  
pp. 343-357 ◽  
Author(s):  
Hideaki Mouri
Keyword(s):  
Energy Dissipation ◽  
Momentum Transfer ◽  
Phenomenological Model ◽  
Correlation Functions ◽  
Wall Turbulence ◽  
Energy Spectra ◽  
Velocity Fluctuations ◽  
Point Correlation ◽  
Stress Layer ◽  
Additional Assumptions

For the constant-stress layer of wall turbulence, two-point correlations of velocity fluctuations are studied theoretically by using the attached-eddy hypothesis, i.e. a phenomenological model of a random superposition of energy-containing eddies that are attached to the wall. While previous studies had invoked additional assumptions, we focus on the minimum assumptions of the hypothesis to derive the most general forms of the correlation functions. They would allow us to use or assess the hypothesis without any effect of those additional assumptions. We also study the energy spectra and the two-point correlations of the rate of momentum transfer and of the rate of energy dissipation.

scholarly journals Experimental investigations of turbulent drag reduction by surface-embedded grooves

2007 ◽  
Vol 590 ◽  
pp. 107-116 ◽  
Author(s):  
B. FROHNAPFEL ◽  
J. JOVANOVIĆ ◽  
A. DELGADO
Keyword(s):  
Drag Reduction ◽  
Functional Space ◽  
Wall Turbulence ◽  
Surface Topology ◽  
Viscous Drag ◽  
Experimental Investigations ◽  
Turbulent Drag Reduction ◽  
Velocity Fluctuations ◽  
Turbulent Drag ◽  
Near Wall Turbulence

Consideration of near-wall turbulence in the functional space that emphasizes the level of anisotropy of the velocity fluctuations not only provides an understanding of th causative physics behind remarkable effects of turbulent drag reduction, but also lead to the logical design of a surface topology which is shown experimentally to be capable o producing a significant reduction of viscous drag which far exceeds what has been achieved so far.

Transitions to different kinds of turbulence in a channel with soft walls

2017 ◽  
Vol 822 ◽  
pp. 267-306 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Reynolds Number ◽  
Travelling Waves ◽  
Fluid Velocity ◽  
Rectangular Channel ◽  
Wall Turbulence ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Wall Displacement ◽  
Experimental Resolution ◽  
Soft Wall

The flow in a rectangular channel with walls made of polyacrylamide gel is experimentally studied to examine the effect of soft walls on transition and turbulence. The bottom wall is fixed to a substrate and the top wall is unrestrained. As the Reynolds number increases, two different flow regimes are observed. The first is the ‘soft-wall turbulence’ (Srinivas & Kumaran,J. Fluid Mech., vol. 780, 2015, pp. 649–686). There is a large increase in the magnitudes of the velocity fluctuations after transition and the fluid velocity fluctuations appear to be non-zero at the soft walls, although higher resolution measurements are required to establish the nature of the boundary dynamics. The fluid velocity fluctuations are symmetric about the centreline of the channel, and they show relatively little downstream variation. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface to within the experimental resolution, but displacement fluctuations parallel to the surface are observed after transition. As the Reynolds number is further increased, there is a second ‘wall-flutter’ transition, which involves visible downstream travelling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of frequency less than approximately$500~\text{rad}~\text{s}^{-1}$are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. The transitions are observed in sequence from a laminar flow at Reynolds number less than 1000 for a channel of height 0.6 mm and from a turbulent flow at a Reynolds number greater than 1000 for a channel of height 1.8 mm.

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