Self-similar mean dynamics in turbulent wall flows

Klewicki, Joseph

doi:10.1017/jfm.2012.626

Cited by 60 publications

(90 citation statements)

References 35 publications

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“…Lindgren et al 2004) and further appears, for example, in the log-law for rough-wall-bounded flows (Jackson 1981), in the overlap formulation for the turbulent channel and pipe flows proposed by Wosnik et al (2000). Recently, similar formulation of the near-wall log-law has been identified by Fife et al (2009) (also see Klewicki 2013). …”

Section: New Viscous Sublayer Velocity Scaling Law For the Suction Wallmentioning

confidence: 69%

New scaling laws for turbulent Poiseuille flow with wall transpiration

2014

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Under consideration for publication in J. Fluid Mech. 1 New Scaling Laws for Turbulent PoiseuilleFlow with Wall Transpiration A fully developed, turbulent Poiseuille flow with wall transpiration, i.e. uniform blowing and suction on the lower and upper walls correspondingly, is investigated by both direct numerical simulation (DNS) of the three-dimensional, incompressible Navier-Stokes equations and Lie symmetry analysis. The latter is used to find symmetry transformations and in turn to derive invariant solutions of the set of two-and multi-point correlation equations. We show that the transpiration velocity is a symmetry breaking which implies a logarithmic scaling law in the core of the channel. DNS validates this result of Lie symmetry analysis and hence aids establishing a new logarithmic law of deficit-type. The region of validity of the new logarithmic law is very different from the usual near-wall log-law and the slope constant in the core region differs from the von Kármán constant and is equal to 0.3. Further, extended forms of the linear viscous sublayer law and the near-wall log-law are also derived, which, as a particular case, include these laws for the classical non-transpirating case. The viscous sublayer at the suction side has an asymptotic suction profile. The thickness of the sublayer increase at high Reynolds and transpiration numbers. For the near-wall log-law we see an indication that it appears at the moderate transpiration rates (0.05 < v 0 /u τ < 0.1) and only at the blowing wall. Finally, from the DNS data we establish a relation between the friction velocity u τ and the transpiration v 0 which turns out to be linear at moderate transpiration rates.

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Section: New Viscous Sublayer Velocity Scaling Law For the Suction Wallmentioning

confidence: 69%

New scaling laws for turbulent Poiseuille flow with wall transpiration

2014

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“…Klewicki and co-authors [5][6][7] have proposed an alternative, four-layer structure based on relative magnitudes of terms in the momentum budget, as observed in direct numerical simulation (DNS) and experimental data. Another potentially useful route is to consider the role of turbulent statistical fluctuations in generating macroscopic phenomena such as the MVP.…”

Section: )mentioning

confidence: 99%

“…30) and is possibly the result of streaks within the buffer region that are known to not scale with distance from the wall. 31 The four-layer model proposed by Klewicki and co-authors [5][6][7] proposes a self-similar region governed by a hierarchy of length-scales linearly related to y + , spanning y + = 2.6 √ Re τ to y = 0.5R. For this DNS dataset, the self-similar region (and associated scaling with y + ) is predicted to begin at y + = 2.6 × √ 2003 = 116, in good agreement with the observed height at which k a+ begins varying with y + in the DNS dataset.…”

Section: B Assumption 2: Idealized Form Of F Vv +mentioning

confidence: 99%

Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

et al. 2016

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A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the “law of the wall”. While the approach reasonably models the MVP’s logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the “missing” curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the “spectral link” between Fvv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.

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“…turbulent channel, pipe and boundary layer flows, predictions of mean profiles continue to remain a challenge (Marusic et al 2010b;Smits & Marusic 2013). There have been numerous theoretical attempts to predict the mean velocity scaling (Wosnik, Castillo & George 2000;Monkewitz, Chauhan & Nagib 2007;Jones, Nickels & Marusic 2008;L'vov, Procaccia & Rudenko 2008;Nagib & Chauhan 2008;Klewicki 2013;Luchini 2017), but much fewer on the Reynolds stresses (including turbulence intensities u u , v v and w w in streamwise x, wall-normal y and spanwise z directions, respectively). For the stresses, an important conceptual model is the wall-attached hypothesis by Townsend (1976).…”

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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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Self-similar mean dynamics in turbulent wall flows

Cited by 60 publications

References 35 publications

New scaling laws for turbulent Poiseuille flow with wall transpiration

New scaling laws for turbulent Poiseuille flow with wall transpiration

Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

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

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