On the large-scale streaks in the logarithmic layer of wall-bounded flows

2021 ◽  
Author(s):  
Jian-Hua Liu ◽  
Nan Jiang ◽  
Leonardo P. Chamorro
Keyword(s):  
Large Scale ◽  
Wall Bounded Flows ◽  
Logarithmic Layer

scholarly journals Simulations of turbulent channels with prescribed velocity profiles

2013 ◽  
Vol 723 ◽  
pp. 587-603 ◽  
Author(s):  
Florian Tuerke ◽  
Javier Jiménez
Keyword(s):  
Large Scale ◽  
Velocity Profiles ◽  
Reynolds Stresses ◽  
Local Character ◽  
Velocity Scale ◽  
Local Shear ◽  
Non Local ◽  
Energy Equilibrium ◽  
Logarithmic Layer ◽  
Local Shear Stress

AbstractDirect numerical simulations of turbulent channels with artificially prescribed velocity profiles are discussed, using both natural and purposely incorrect profiles. It is found that turbulence develops correctly when natural profiles are prescribed, but that even slightly incorrect ones modify the Reynolds stresses substantially. That is used to study the dynamics of the energy-containing velocity fluctuations. The stronger (weaker) structures generated by locally stronger (weaker) mean shears have essentially correct isotropy coefficients but they are out of energy equilibrium, with the energy imbalance compensated by turbulent diffusion. The velocity scale in smooth profiles changes with the distance to the wall, and is best described by a friction velocity derived from the local total tangential stress. The behaviour across sharper shear jumps is more consistent with non-equilibrium eddies that relax over wall-normal distances of the order of the distance to the wall, suggesting that the energy equilibrium in the logarithmic layer is not local to a given height, but applies to extended layers homogenized by wall-normal fluxes. Examples of that non-local character are the large-scale inactive fluctuations near the wall, whose velocities do not scale with the local shear stress, but with that of their active ‘cores’ farther away from the wall.

Wall shear stress and velocity in a turbulent axisymmetric boundary layer

1994 ◽  
Vol 259 ◽  
pp. 191-218 ◽  
Author(s):  
Anthony Wietrzak ◽  
Richard M. Lueptow
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Large Scale ◽  
Low Frequency ◽  
Streamwise Velocity ◽  
Outer Flow ◽  
Planar Wall ◽  
Wall Bounded Flows ◽  
Wall Shear

Instantaneous streamwise fluctuations of the wall shear stress have been measured using a hot-element probe in a thick axisymmetric turbulent boundary layer on a cylinder aligned parallel to the flow. The measurements were made at a momentum-thickness Reynolds number Rθ = 3050 and a ratio of boundary-layer thickness to cylinder radius of δ/a = 5.7. The ratio of the r.m.s. of the fluctuation to the mean value of the wall shear stress, $\tau_{rms}/\bar{\tau}$, is about 0.32, a value slightly lower than that for recent measurements for flow over a flat plate. The probability density function of the wall shear stress is similar to that for planar wall-bounded flows within experimental error. The power spectral density of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Analysis of simultaneous measurement of the streamwise wall shear stress and the streamwise velocity using VITA and peak detection suggests that transverse curvature has little effect on the near-wall burst–sweep cycle compared to planar wall-bounded flows. The angle of inclination of the structures is similar to that measured for large-scale structures in planar wall-bounded flows. However, measurements of the cross-correlation between the shear stress and the velocity suggest the existence of smaller structures yawed to the axis of the cylinder. The coherence between shear stress and velocity shows a low frequency associated with the inclined structures and a higher frequency associated with the yawed structures. The yawed structures could have an arrowhead or half-arrowhead shape and may be associated with fluid from the outer flow washing over the cylinder.

scholarly journals Spatial modulations of kinetic energy in the roughness sublayer

2018 ◽  
Vol 850 ◽  
pp. 584-610 ◽  
Author(s):  
Jérémy Basley ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Kinetic Energy ◽  
Outer Layer ◽  
Large Scale ◽  
Stereoscopic Particle Image Velocimetry ◽  
Spatial Modulation ◽  
Roughness Sublayer ◽  
Small Scale ◽  
Smooth Wall ◽  
Wall Bounded Flows ◽  
Scale Turbulence

High-Reynolds-number experiments are conducted in the roughness sublayer of a turbulent boundary layer developing over a cubical canopy. Stereoscopic particle image velocimetry is performed in a wall-parallel plane to evidence a high degree of spatial modulation of the small-scale turbulence around the footprint of large-scale motions, despite the suppression of the inner layer by the high roughness elements. Both Fourier and wavelets analyses show that the near-wall cycle observed in smooth-wall-bounded flows is severely disrupted by the canopy, whose wake in the roughness sublayer generates a new range of scales, closer to that of the outer-layer large-scale motions. This restricts significantly scale separation, hence a diagnostic method is developed to divide carefully and rationally the fluctuating velocity fields into large- and small-scale components. Our analysis across all turbulent kinetic energy terms sheds light on the spatial imprint of the modulation mechanism, revealing a very different signature on each velocity component. The roughness sublayer shows a preferential arrangement of the modulated scales similar to what is observed in the outer layer of smooth-wall-bounded flows – small-scale turbulence is enhanced near the front of high momentum regions and damped at the front of low momentum regions. More importantly, accessing spanwise correlations reveals that modulation intensifies the most along the flanks of the large-scale motions.

Azimuthal structure of turbulence in high Reynolds number pipe flow

2008 ◽  
Vol 615 ◽  
pp. 121-138 ◽  
Author(s):  
SEAN C. C. BAILEY ◽  
MARCUS HULTMARK ◽  
ALEXANDER J. SMITS ◽  
MICHAEL P. SCHULTZ
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Pipe Flow ◽  
Roughness Effects ◽  
Azimuthal Correlations ◽  
Normal Distance ◽  
Logarithmic Layer ◽  
High Reynolds

Two-point hot-wire measurements of streamwise velocity were performed in the logarithmic and wake regions of turbulent pipe flow for Reynolds numbers, based on pipe diameter, ranging from 7.6 × 104 to 8.3 × 106 at four wall-normal positions with azimuthal probe separation. The azimuthal correlations were found to be consistent with the presence of very large-scale coherent regions of low-wavenumber, low-momentum fluid observed in previous studies of wall-bounded flows and were found to be independent of changing Reynolds number and surface roughness effects. At the edge of the logarithmic layer the azimuthal scale determined from the correlations was found to be similar to that observed for channel flows but larger than that observed for boundary layers, inconsistent with the concept of a universal logarithmic region. As the wall-normal position increased outside the logarithmic layer, there was a decrease in azimuthal scale relative to that of channel flow. Using cross-spectral analysis, high-wavenumber motion was found to grow azimuthally with wall-normal distance at a faster rate than the low-wavenumber motions.

scholarly journals Vortex organization in the outer region of the turbulent boundary layer

2000 ◽  
Vol 422 ◽  
pp. 1-54 ◽  
Author(s):  
R. J. ADRIAN ◽  
C. D. MEINHART ◽  
C. D. TOMKINS
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Spatial Coherence ◽  
Three Dimensional ◽  
Outer Region ◽  
Wall Layer ◽  
Velocity Fields ◽  
Streamwise Direction ◽  
Hairpin Vortices ◽  
Logarithmic Layer

The structure of energy-containing turbulence in the outer region of a zero-pressure- gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 < Reθ < 6845 show that the boundary layer is densely populated by velocity fields associated with hairpin vortices. (The term ‘hairpin’ is here taken to represent cane, hairpin, horseshoe, or omega-shaped vortices and deformed versions thereof, recognizing these structures are variations of a common basic flow structure at different stages of evolution and with varying size, age, aspect ratio, and symmetry.) The signature pattern of the hairpin consists of a spanwise vortex core located above a region of strong second-quadrant fluctuations (u < 0 and v > 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

scholarly journals Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows

2017 ◽  
Vol 830 ◽  
pp. 797-819 ◽  
Author(s):  
Dominik Krug ◽  
Xiang I. A. Yang ◽  
Charitha M. de Silva ◽  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Velocity Component ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Structure Functions ◽  
Self Similarity ◽  
Moderate Reynolds Number ◽  
Taylor Couette ◽  
Wall Bounded Flows ◽  
Universal Behaviour

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498–510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor–Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework – both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.

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