On the scaling of three-dimensional homogeneous and isotropic turbulence

Benzi, Roberto; Ciliberto, S.; Baudet, Christophe; Chavarría, Gerardo Ruiz

doi:10.1016/0167-2789(94)00190-2

Cited by 210 publications

(243 citation statements)

References 14 publications

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“…Moreover, comparison of singlepoint statistics in the ECR in turbulent boundary layers and channel flows (Sillero et al 2013) and the analysis of the second-order structure function in pipe flows (Chung et al 2015) suggest that differences with regard to (1.3) exist in different flow geometries. However, borrowing inspiration from the original ESS analysis of Benzi et al (1993Benzi et al ( , 1995, de Silva et al (2017) were recently able to demonstrate universality for the ECR Statistics of turbulence in the energy-containing range 3 scales in wall-bounded flows. In particular, they showed that when evaluating S p (s x ; u x ) with respect to a reference structure function S m (s x ; u x ) ≡ (∆u + x ) 2m 1/m of arbitrary order 2m, the 'ESS-form' of (1.3), given by 4) holds over a larger range of wall distances and at significantly lower Re τ than the direct representation (1.3).…”

Section: Introductionmentioning

confidence: 99%

“…Anselmet et al 1984;Frisch 1995). To firmly establish the universality of the ISR statistics, the so-called extended self-similarity (ESS) hypothesis of Benzi et al (1993Benzi et al ( , 1995 played a central role (Arneodo et al 1996;Belin et al 1996). In this framework, instead of evaluating the scaling of the structure functions directly as a function of distance, the relative scaling exponent is sought by plotting one structure function against another one of different order on log-log scales.…”

Section: Introductionmentioning

confidence: 99%

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

Krug¹,

Yang²,

Silva³

et al. 2017

J. Fluid Mech.

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Krug¹,

Yang²,

Silva³

et al. 2017

J. Fluid Mech.

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“…(In particular, Praskovsky and Onsley [112] found that £ 2 is close to zero at all inspected by them values of Re x , and there are also other authors who supposed that the available data are insufficient for proving that £ 2 * 0.) Barenblatt et al [118] tried to use for the verification of their assumption about the dependence of a = £ 2 on Re the data by Benzi et al [119] who measured the values of functions D 2 (r) and D 3 (r) in four different flows with Re = 5000, 6000, 18 000, and 300 000 (where different definitions of Re were used for different flows). In [119] it was found that to the summary collection of all obtained data corresponded the practically constant correction £ 2 =0.03.…”

Section: Kolmogorov's Theory Of Locally Isotropie Turbulencementioning

confidence: 99%

“…Barenblatt et al [118] tried to use for the verification of their assumption about the dependence of a = £ 2 on Re the data by Benzi et al [119] who measured the values of functions D 2 (r) and D 3 (r) in four different flows with Re = 5000, 6000, 18 000, and 300 000 (where different definitions of Re were used for different flows). In [119] it was found that to the summary collection of all obtained data corresponded the practically constant correction £ 2 =0.03. Barenblatt et al separated data points corresponding to individual experiments and their processing of four separate (rather small) groups of points led to conclusion that the corrections £ 2 differ in the cases of different experiments decreasing with the growth of Re and possibly tending to zero as Re ->°o.…”

Section: Kolmogorov's Theory Of Locally Isotropie Turbulencementioning

confidence: 99%

“…All the measurements of these exponents are rather crude and their results may depend on the choice of the 'inertial range' where the structure functions satisfy the power laws. Note also that in [119][120][121] the scaling exponents were determined indirectly basing on the 'extended self-similarity' (ESS) hypothesis by Benzi et al [119] generalizing the concept of the inertial range where structure functions D n (r) satisfy power laws (17). Eq.…”

Section: Kolmogorov's Theory Of Locally Isotropie Turbulencementioning

confidence: 99%

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The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

Yaglom¹

Les Houches - Ecole D’Ete De Physique Theorique

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Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

1998

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A multifractal method describing the fine-scale structure of turbulence, including its intermittency, is applied to derive the drop breakage functions for drops whose diameter falls within the inertial subrange of turbulence, including effects of the viscosity of the dispersed phase. The model predicts well the transient drop size distributions of dispersions undergoing breakage at long stirring times. Concepts of quasi-stable and asymptotically stable drop sizes are presented and discussed in relation to the exponent on the Weber number. The functions for drop break-up in the viscous subrange are proposed and discussed.On applique une mCthode multifractale dCcrivant la structure fine de la turbulence, incluant son intermittence, afin de calculer les fonctions de rupture des gouttes B partir de gouttes dont le diamttre correspond au sous-domaine inertiel de turbulence, incluant les effets de la viscositt de la phase disperske. Le modtle prtdit convenablement les distributions de tailles de gouttes transitoires des dispersions subissant une rupture h des temps de mClange longs. Des concepts de tailles de gouttes quasi stables et asymptotiquement stables sont prtsentts et examints par rapport h l'exposant du nombre de Weber. Les fonctions pour la rupture des gouttes dans le sous-domaine visqueux sont proposCes et analystes.Keywords: breakage, intermittency, multifractal distribution, transient drop size distribution, turbulence.drop, suspended in a continuous phase, breaks up if the A local instantaneous stresses generated by turbulent motions in the continuous phase exceed the stabilizing forces due to the interfacial tension and the drop viscosity. In the present paper the authors are interested in the phenomenon of turbulent dispersion of droplets for some practical as well as theoretical reasons. Liquid-liquid dispersions are of importance to industry, as they are involved with many engineering operations including extraction, chemical reaction, emulsion and suspension polymerization etc. From the theoretical point of view, investigation of relations between turbulence and droplet breakage can help to understand the question, how the fluid mechanical forces induced by turbulence cause drop break-up. Understanding of this phenomenon should enable construction of the mathematical models able to predict the transient drop size distributions and the diameter of the largest stable drops. The droplet size distribution and its rate of evolution are determined by the processes of drop breakage and coalescence. In this paper we are interested in drop break-up, hence we shall confine our considerations to experimental conditions under which drop sizes are not influenced by coalescence. To this end one should consider low concentrations of the dispersed phase and, possibly, a soluble dispersant in an aqueous phase.The phenomenon of drop dispersion has been a subject of many studies starting from the fundamental papers by Kolmogorov (1949) and Hinze (1955). In these studies the fine-scale turbulence is interpreted by using...

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On the scaling of three-dimensional homogeneous and isotropic turbulence

Cited by 210 publications

References 14 publications

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

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

The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

Drop break‐up in intermittent turbulence: Maximum stable and transient sizes of drops

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