Modification of the large-scale features of high Reynolds number wall turbulence by passive surface obtrusions

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.

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Enhanced wall turbulence model for flow over cylinder at high Reynolds number

AIP Advances ◽

10.1063/1.5118421 ◽

2019 ◽

Vol 9 (9) ◽

pp. 095012 ◽

Cited By ~ 2

Author(s):

A. Aravind Raghavan Sreenivasan ◽

B. Kannan Iyer

Keyword(s):

Reynolds Number ◽

Turbulence Model ◽

High Reynolds Number ◽

Wall Turbulence ◽

Flow Over Cylinder ◽

High Reynolds

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The variation of large-scale structure inclination angles in high Reynolds number atmospheric surface layers

Physics of Fluids ◽

10.1063/1.4978803 ◽

2017 ◽

Vol 29 (3) ◽

pp. 035104 ◽

Cited By ~ 21

Author(s):

Hong-You Liu ◽

Tian-Li Bo ◽

Yi-Rui Liang

Keyword(s):

Reynolds Number ◽

High Reynolds Number ◽

Large Scale ◽

Large Scale Structure ◽

Scale Structure ◽

Surface Layers ◽

Inclination Angles ◽

High Reynolds

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Fine Structure of Vortex Sheet Rollup by Viscous and Inviscid Simulation

Journal of Fluids Engineering ◽

10.1115/1.2926492 ◽

1991 ◽

Vol 113 (1) ◽

pp. 31-36 ◽

Cited By ~ 44

Author(s):

G. Tryggvason ◽

W. J. A. Dahm ◽

K. Sbeih

Keyword(s):

Reynolds Number ◽

High Reynolds Number ◽

Large Scale ◽

Stokes Equations ◽

Flow Region ◽

Vortex Sheet ◽

Navier Stokes ◽

Vortex Sheets ◽

Limiting Behavior ◽

High Reynolds

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

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

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0077 ◽

2017 ◽

Vol 375 (2089) ◽

pp. 20160077 ◽

Cited By ~ 20

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’.

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