Intermittency and rough-pipe turbulence

Mehrafarin, Mohammad; Pourtolami, Nima

doi:10.1103/physreve.77.055304

Cited by 23 publications

(21 citation statements)

References 17 publications

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“…Thus, we have been able to draw support for the classic laws from empirical data unrelated to the MVPs. From a broader perspective, our derivation indicates that, contrary to what might be inferred from the standard derivation of the classic laws, the MVPs as well as the attendant phenomenon of turbulent friction are inextricably linked to, and can indeed be interpreted as macroscopic manifestations of, the spectrum of turbulent energy [7,[13][14][15][16][17][18][19][20].…”

Section: Discussioncontrasting

confidence: 66%

Spectral derivation of the classic laws of wall-bounded turbulent flows

Gioia¹,

Chakraborty²

2017

Proc. R. Soc. A.

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We show that the classic laws of the mean-velocity profiles (MVPs) of wall-bounded turbulent flows—the ‘law of the wall,’ the ‘defect law’ and the ‘log law’—can be predicated on a sufficient condition with no manifest ties to the MVPs, namely that viscosity and finite turbulent domains have a depressive effect on the spectrum of turbulent energy. We also show that this sufficient condition is consistent with empirical data on the spectrum and may be deemed a general property of the energetics of wall turbulence. Our findings shed new light on the physical origin of the classic laws and their immediate offshoot, Prandtl’s theory of turbulent friction.

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Section: Discussioncontrasting

confidence: 66%

Spectral derivation of the classic laws of wall-bounded turbulent flows

Gioia¹,

Chakraborty²

2017

Proc. R. Soc. A.

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“…In this expression, η is the intermittency exponent, which arises as an anomalous scaling exponent characterizing the average dissipation over a neighbourhood whose dimension is . To see how incomplete similarity modifies the scaling law for the friction factor, we present an argument due to Mehrafarin and Pourtolami [57], that is in the spirit of Kadanoff's block spin construction [44]. The friction factor is assumed to depend on δv and the mean flow speed in the pipe U through a decomposition of the Reynolds stress…”

Section: Anomalous Dimensions In Turbulencementioning

confidence: 99%

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Goldenfeld

Shih

2016

J Stat Phys

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The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a nonequilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.

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“…Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations. 16,17 Turbulent flows past a wall experience frictional drag, the macroscopic property of a flow that sets the cost of pumping oil through a pipeline, the draining capacity of a river in flood, and other quantities of engineering interest 2,3,5,18,19 . The frictional drag is defined as the dimensionless ratio f = τ /ρU 2 , where τ is the shear stress or force per unit area that develops between the flow and the wall, ρ is the density of the fluid, and U is the mean velocity of the flow.…”

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confidence: 99%

Macroscopic effects of the spectral structure in turbulent flows

et al. 2010

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Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure

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Intermittency and rough-pipe turbulence

Cited by 23 publications

References 17 publications

Spectral derivation of the classic laws of wall-bounded turbulent flows

Spectral derivation of the classic laws of wall-bounded turbulent flows

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Macroscopic effects of the spectral structure in turbulent flows

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