Large- and very-large-scale motions in channel and boundary-layer flows

2007 ◽  
Vol 365 (1852) ◽  
pp. 665-681 ◽  
Author(s):  
B.J Balakumar ◽  
R.J Adrian
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pipe Flow ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Boundary Layer Flows ◽  
Wall Flows ◽  
Large Structures ◽  
Measurement And Analysis ◽  
Common Behaviour

Large-scale motions (LSMs; having wavelengths up to 2–3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-large-scale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.

Very-large-scale motions in a turbulent boundary layer

2011 ◽  
Vol 673 ◽  
pp. 80-120 ◽  
Author(s):  
JAE HWA LEE ◽  
HYUNG JIN SUNG
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Spatial Organization ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Hairpin Vortices ◽  
Extraction Algorithm ◽  
Normal Distance

Direct numerical simulation of a turbulent boundary layer was performed to investigate the spatially coherent structures associated with very-large-scale motions (VLSMs). The Reynolds number was varied in the range Reθ = 570–2560. The main simulation was conducted by using a computational box greater than 50δo in the streamwise domain, where δo is the boundary layer thickness at the inlet, and inflow data was obtained from a separate inflow simulation based on Lund's method. Inspection of the three-dimensional instantaneous fields showed that groups of hairpin vortices are coherently arranged in the streamwise direction and that these groups create significantly elongated low- and high-momentum regions with large amounts of Reynolds shear stress. Adjacent packet-type structures combine to form the VLSMs; this formation process is attributed to continuous stretching of the hairpins coupled with lifting-up and backward curling of the vortices. The growth of the spanwise scale of the hairpin packets occurs continuously, so it increases rapidly to double that of the original width of the packets. We employed the modified feature extraction algorithm developed by Ganapathisubramani, Longmire & Marusic (J. Fluid Mech., vol. 478, 2003, p. 35) to identify the properties of the VLSMs of hairpin vortices. In the log layer, patches with the length greater than 3δ–4δ account for more than 40% of all the patches and these VLSMs contribute approximately 45% of the total Reynolds shear stress included in all the patches. The VLSMs have a statistical streamwise coherence of the order of ~6δ; the spatial organization and coherence decrease away from the wall, but the spanwise width increases monotonically with the wall-normal distance. Finally, the application of linear stochastic estimation demonstrated the presence of packet organization in the form of a train of packets in the log layer.

Statistical structure of turbulent-boundary-layer velocity–vorticity products at high and low Reynolds numbers

2007 ◽  
Vol 570 ◽  
pp. 307-346 ◽  
Author(s):  
P. J. A. PRIYADARSHANA ◽  
J. C. KLEWICKI ◽  
S. TREAT ◽  
J. F. FOSS
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Rough Wall ◽  
Reynolds Stresses ◽  
Wall Boundary Layer ◽  
Layer Flow

The mean wall-normal gradients of the Reynolds shear stress and the turbulent kinetic energy have direct connections to the transport mechanisms of turbulent-boundary-layer flow. According to the Stokes–Helmholtz decomposition, these gradients can be expressed in terms of velocity–vorticity products. Physical experiments were conducted to explore the statistical properties of some of the relevant velocity–vorticity products. The high-Reynolds-number data (Rθ≃O(106), where θ is the momentum thickness) were acquired in the near neutrally stable atmospheric-surface-layer flow over a salt playa under both smooth- and rough-wall conditions. The low-Rθdata were from a database acquired in a large-scale laboratory facility at 1000 >Rθ> 5000. Corresponding to a companion study of the Reynolds stresses (Priyadarshana & Klewicki,Phys. Fluids, vol. 16, 2004, p. 4586), comparisons of low- and high-Rθas well as smooth- and rough-wall boundary-layer results were made at the approximate wall-normal locationsyp/2 and 2yp, whereypis the wall-normal location of the peak of the Reynolds shear stress, at each Reynolds number. In this paper, the properties of thevωz,wωyanduωzproducts are analysed through their statistics and cospectra over a three-decade variation in Reynolds number. Hereu,vandware the fluctuating streamwise, wall-normal and spanwise velocity components and ωyand ωzare the fluctuating wall-normal and spanwise vorticity components. It is observed thatv–ωzstatistics and spectral behaviours exhibit considerable sensitivity to Reynolds number as well as to wall roughness. More broadly, the correlations between thevand ω fields are seen to arise from a ‘scale selection’ near the peak in the associated vorticity spectra and, in some cases, near the peak in the associated velocity spectra as well.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

Turbulence structure of a reattaching mixing layer

1981 ◽  
Vol 110 ◽  
pp. 171-194 ◽  
Author(s):  
C. Chandrsuda ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Flow Region ◽  
Turbulent Energy ◽  
Turbulence Structure ◽  
Hot Wire ◽  
Recirculating Flow

Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Large-scale modes of turbulent channel flow: transport and structure

2001 ◽  
Vol 448 ◽  
pp. 53-80 ◽  
Author(s):  
Z. LIU ◽  
R. J. ADRIAN ◽  
T. J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Upstream Region ◽  
Two Dimensional ◽  
Normal Plane

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

scholarly journals Letter: The link between the Reynolds shear stress and the large structures of turbulent Couette-Poiseuille flow

2018 ◽  
Vol 30 (4) ◽  
pp. 041702 ◽  
Author(s):  
Sergio Gandía-Barberá ◽  
Sergio Hoyas ◽  
Martin Oberlack ◽  
Stefanie Kraheberger
Keyword(s):  
Shear Stress ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Large Structures

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

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