New perspective in statistical modeling of wall-bounded turbulence

She, Zhen‐Su; Chen, Xi; Wu, You; Hussain, Fazle

doi:10.1007/s10409-010-0391-y

Cited by 48 publications

(30 citation statements)

References 34 publications

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“…Finally, owing to the universal nature of wall dilation symmetry, the analysis is applicable to many other wall flows with different flow conditions, such as incompressible (Wu et al 2013;Chen & She 2016) and compressible TBL (She et al 2010;Zhang et al 2012;Wu et al 2017), roughness effects , with and without mild pressure gradients, and turbulent Rayleigh-Bénard convection (to be communicated soon). The results have also been extended to improve turbulent engineering models (Chen et al 2015(Chen et al , 2016a.…”

Section: Discussionmentioning

confidence: 99%

Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses

2018

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We present new scaling expressions, including high-Reynolds-number (Re) predictions, for all Reynolds stress components in the entire flow domain of turbulent channel and pipe flows. In Part 1 (She et al., J. Fluid Mech., vol. 827, 2017, pp. 322-356), based on the dilation symmetry of the mean Navier-Stokes equation a four-layer formula of the Reynolds shear stress length 12 -and hence also the entire mean velocity profile (MVP) -was obtained. Here, random dilations on the second-order balance equations for all the Reynolds stresses (shear stress −u v , and normal stresses u u , v v , w w ) are analysed layer by layer, and similar four-layer formulae of the corresponding stress length functions 11 , 22 , 33 (hence the three turbulence intensities) are obtained for turbulent channel and pipe flows. In particular, direct numerical simulation (DNS) data are shown to agree well with the four-layer formulae for 12 and 22 -which have the celebrated linear scalings in the logarithmic layer, i.e. 12 ≈ κy and 22 ≈ κ 22 y.

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Section: Discussionmentioning

confidence: 99%

Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses

2018

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“…The success of vw indicates the validity of the concept of the ''order function'' (here a u i u j ) in identifying the multilayer structure in wall turbulence, which has been well tested in the study of incompressible channel or pipe and boundary layer flows [16][17][18]. These studies suggest that the multilayer structure is the result of symmetry breaking in the mean field induced by turbulent fluctuations and the order functions capture the transitions between different layer states.…”

Section: Fig 3 (Color Online) Global M Invariance Of Density Viscosmentioning

confidence: 99%

Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Zhang

Hussain

et al. 2012

Phys. Rev. Lett.

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A series of Mach-number-(M) invariant scalings is derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean-velocity profile that is superior to van Driest transformation. The theory is validated by direct numerical simulation of spatially developing CTBLs with M up to 6. A boundary layer edge is introduced to compare different M flows and is shown to better present the M-invariant multilayer structure of CTBLs. The new scalings derived from the kinetic energy balance substantiate Morkovin's hypothesis and promise accurate prediction of the mean profiles of CTBLs.

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“…The original idea was presented in [10] and formulated rigorously in [11]. The goal of the theory is to find invariant solutions of the averaged flow equations based on a symmetry analysis of a set of new quantities, called order functions, which are introduced in close analogy to order parameter [12] in the study of critical phenomena.…”

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Anomalous dissipation and kinetic-energy distribution in pipes at very high Reynolds numbers

et al. 2016

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A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over a wide range of Re yield 0.45 to be the universal Karman constant. A new spatial invariant characterizing outer dynamics is discovered and validated by reliable experimental data. The theory predicts the mean velocity profile (MVP) with 99% accuracy for high Re experimental data (up to 40 millions), and offers a quantitative explanation for recent observation of logarithmic kinetic energy distribution by Hullmak et al. (Phys. Rev. Lett. 108, 094501).Turbulent flows over objects form thin vorticity layers called boundary layers. As it is widely accepted that near-wall flow physics is autonomous and independent of the flow being external or internal, pipe flow forms an experimentally and numerically expedient canonical flow for the study of wall turbulence. Despite extensive efforts, the prediction of the mean velocity still relies on empirical functions [1] having limited accuracy and limited range of Reynolds numbers (Re). Hence, the problem continues to receive vivid attention with great experimental [2,3] and theoretical [4] efforts.From a statistical physics point of view, turbulent pipe flows are at a far-from-equilibrium state encompassing not only a cross-scale energy flux (cascade) but also momentum and energy fluxes in space. Understanding physical principles governing the non-homogeneous transport and non-uniform distribution of the mean momentum and kineticenergy is a log-standing goal of the research. Nearly eighty years ago, Prandtl [5] and von Karman [6], independently proposed the concept of mixing length with a linear dependence on the distance from the wall, predicting a logarithmic MVP and hence friction coefficient. However, this empirical model has led to controversies: Barenblatt et al [7] have claimed that power-law is a better description; Goldenfeld [8] has proposed a model for friction coefficient using a power-law description. A recent model of L 'vov et al. [4] is particularly noteworthy, as its log-law description yields predictions of reasonable accuracy over a range of finite Re (see Fig.2). Recently, a logarithmic scaling for the streamwise mean kinetic energy profile (MKP) is reported [9], with no explanation. Clearly, a deductive theory for joint MVP and MKP is still missing.Here, we present a Lie-group based similarity theory for turbulent channel and pipe flows. The original idea was presented in [10] and formulated rigorously in [11]. The goal of the theory is to find invariant solutions of the averaged flow equations based on a symmetry analysis of a set of new quantities, called order functions, which are introduced in close analogy to order parameter [12] in the study of critical phenomena. Adding the order function to dependent variables in the equations and then performing a dilation-group transformation yields a set of new, candidate i...

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New perspective in statistical modeling of wall-bounded turbulence

Cited by 48 publications

References 34 publications

Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses

Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses

Mach-Number-Invariant Mean-Velocity Profile of Compressible Turbulent Boundary Layers

Anomalous dissipation and kinetic-energy distribution in pipes at very high Reynolds numbers

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