On the Large-scale Flow Motions in Fully Developed Turbulent Channel Flow (2nd Report, Effect of Thermal Stratification and Self-similarity)

The relation between Eulerian structure function’s scaling exponents and Lagrangian ones in turbulent channel flows is explored both theoretically and numerically. A nonlinear parametric transformation between Eulerian structure function’s scaling exponents and Lagrangian ones is derived, following Landau and Novikov’s frame work. This relation is then compared to some known experimental and numerical results, but mainly to our DNS (direct numerical simulation) results of a fully developed channel flow with Reτ = 100. The scaling exponents are evaluated in terms of the ESS (extended self-similarity) method, since the Reynolds number is too low to make the standard scaling laws applicable. The agreement between theory and simulation is satisfactory

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Coherent structures in the linearized impulse response of turbulent channel flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.15 ◽

2019 ◽

Vol 863 ◽

pp. 1190-1203 ◽

Cited By ~ 9

Author(s):

Sabarish B. Vadarevu ◽

Sean Symon ◽

Simon J. Illingworth ◽

Ivan Marusic

Keyword(s):

Channel Flow ◽

Coherent Structures ◽

Large Scale ◽

Body Force ◽

Stokes Equations ◽

Turbulent Channel Flow ◽

Kinetic Energy Density ◽

Reynolds Stresses ◽

Mean Velocity ◽

Velocity Fluctuations

We study the evolution of velocity fluctuations due to an isolated spatio-temporal impulse using the linearized Navier–Stokes equations. The impulse is introduced as an external body force in incompressible channel flow at $Re_{\unicode[STIX]{x1D70F}}=10\,000$. Velocity fluctuations are defined about the turbulent mean velocity profile. A turbulent eddy viscosity is added to the equations to fix the mean velocity as an exact solution, which also serves to model the dissipative effects of the background turbulence on large-scale fluctuations. An impulsive body force produces flow fields that evolve into coherent structures containing long streamwise velocity streaks that are flanked by quasi-streamwise vortices; some of these impulses produce hairpin vortices. As these vortex–streak structures evolve, they grow in size to be nominally self-similar geometrically with an aspect ratio (streamwise to wall-normal) of approximately 10, while their kinetic energy density decays monotonically. The topology of the vortex–streak structures is not sensitive to the location of the impulse, but is dependent on the direction of the impulsive body force. All of these vortex–streak structures are attached to the wall, and their Reynolds stresses collapse when scaled by distance from the wall, consistent with Townsend’s attached-eddy hypothesis.

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Nonlinear optimal large-scale structures in turbulent channel flow

European Journal of Mechanics - B/Fluids ◽

10.1016/j.euromechflu.2018.04.016 ◽

2018 ◽

Vol 72 ◽

pp. 74-86 ◽

Cited By ~ 1

Author(s):

M. Farano ◽

S. Cherubini ◽

P. De Palma ◽

J.-C. Robinet

Keyword(s):

Channel Flow ◽

Large Scale ◽

Turbulent Channel Flow ◽

Large Scale Structures ◽

Scale Structures

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Model Simulations of Large-Scale Structures in Turbulent Channel Flow.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B ◽

10.1299/kikaib.69.377 ◽

2003 ◽

Vol 69 (678) ◽

pp. 377-384

Author(s):

Koichi TSUJIMOTO ◽

Yutaka MIYAKE ◽

Mitsugu OKUDA

Keyword(s):

Channel Flow ◽

Large Scale ◽

Turbulent Channel Flow ◽

Model Simulations ◽

Large Scale Structures ◽

Scale Structures

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Extended Self-Similarity in Drag-Reduced Turbulent Flow of Viscoelastic Fluid

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C ◽

10.1115/fedsm-icnmm2010-30351 ◽

2010 ◽

Author(s):

Feng-Chen Li ◽

Hong-Na Zhang ◽

Wei-Hua Cai ◽

Juan-Cheng Yang

Keyword(s):

Channel Flow ◽

Viscoelastic Fluid ◽

Isotropic Turbulence ◽

Scaling Law ◽

Viscoelastic Fluids ◽

Turbulent Channel Flow ◽

Elastic Model ◽

Homogeneous Isotropic Turbulence ◽

Self Similarity ◽

Extended Self

Direct numerical simulations (DNS) have been performed for drag-reduced turbulent channel flow with surfactant additives and forced homogeneous isotropic turbulence with polymer additives. Giesekus constitutive equation and finite extensible nonlinear elastic model with Peterlin closure were used to describe the elastic stress tensor for both cases, respectively. For comparison, DNS of water flows for both cases were also performed. Based on the DNS data, the extended self-similarity (ESS) of turbulence scaling law is investigated for water and viscoelastic fluids in turbulent channel flow and forced homogeneous isotropic turbulence. It is obtained that ESS still holds for drag-reduced turbulent flows of viscoelastic fluids. In viscoelastic fluid flows, the regions at which δu(r)∝r and Sp(r)∝S3(r)ζ(p) with ζ(p) = p/3, where r is the scale length, δu(r) is the longitudinal velocity difference along r and Sp(r) is the pth-order moment of velocity increments, in the K41 (Kolmogorov theory)-fashioned plots and ESS-fashioned plots, respectively, are all broadened to larger scale for all the investigated cases.

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Mixing of two thermal fields emitted from line sources in turbulent channel flow

Journal of Fluid Mechanics ◽

10.1017/s0022112008002425 ◽

2008 ◽

Vol 609 ◽

pp. 349-375 ◽

Cited By ~ 15

Author(s):

E. COSTA-PATRY ◽

L. MYDLARSKI

Keyword(s):

Correlation Coefficient ◽

Channel Flow ◽

Large Scale ◽

Turbulent Channel Flow ◽

Separation Distance ◽

Wall Region ◽

Thermal Plume ◽

Passive Scalars ◽

Thermal Fields ◽

Fast Evolution

The interaction of two passive scalars (both temperature in air) emitted from concentrated line sources in fully developed high-aspect-ratio turbulent channel flow is studied. The thermal fields are measured using cold-wire thermometry in a flow with a Reynolds number (Uh/ν) of 10200.The transverse total root-mean-square (RMS) temperature profiles are a function of the separation distance between the line sources (d/h), their average wall-normal position (ysav/h), and the downstream location (x/h), measured relative to the line sources. Similarly, profiles of the non-dimensional form of the scalar covariance, the correlation coefficient (ρ), are a function of the same parameters and quantify the mixing of the two scalars.The transverse profiles of the correlation coefficient are generally largest at the edges of the thermal plume and smallest in its core. When the line sources are not symmetrically located about the channel centreline, the minimum in the correlation coefficient transverse profiles drifts towards the (closer) channel wall. For source locations that are equidistant from the channel centreline, the minimum correlation coefficient occurs at the centreline, due to the underlying symmetry of this geometry. The initial downstream evolution of the correlation coefficient depends significantly on d/h, similar to that in homogeneous turbulence. However, there is always a dependence on ysav/h, which increases in importance as both the downstream distance is increased and the wall is approached. Lastly, the correlation coefficient profiles tend towards positive values in the limit of large downstream distances (relative to the source separation), though further measurements farther downstream are required to confirm the exact value(s) of their asymptotic limit(s).Spectral analysis of the cospectra and coherency spectra indicates that the large scales evolve more rapidly than the small ones. Furthermore, the fast evolution of the large scales was most evident when the sources were located close to the wall. This presumably derives from the large-scale nature of turbulence production, which is strong in the near-wall region.

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Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.697 ◽

2017 ◽

Vol 832 ◽

pp. 483-513 ◽

Cited By ~ 16

Author(s):

Matteo de Giovanetti ◽

Hyung Jin Sung ◽

Yongyun Hwang

Keyword(s):

Channel Flow ◽

Large Scale ◽

Vortical Structure ◽

Outer Region ◽

Turbulent Channel Flow ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

Hairpin Vortices ◽

Large Scale Motion ◽

Scale Motion

It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an ‘amplified’ streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$ where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of $\unicode[STIX]{x1D706}_{x}/h\simeq 1{-}5$ ($h$ is the half-height of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuous-mode instability of the streak, a subprocess of the self-sustaining mechanism of the large-scale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the large-scale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of very-large-scale motion.

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