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Journal ArticleDOI

Measurements of the Small-Scale Structure of Turbulence at Moderate Reynolds Numbers

01 Aug 1970-Physics of Fluids (American Institute of PhysicsAIP)-Vol. 13, Iss: 8, pp 1962-1969
TL;DR: In this article, the first two time derivatives of the streamwise velocity fluctuation in a mixing layer are presented, and the probability distributions of squared derivatives are found to be nearly log normal.
Abstract: Measurements of probability densities and distributions, moments, and spectra obtained from the first two time derivatives of the streamwise velocity fluctuation in a mixing layer are presented. Probability distributions of squared derivatives are found to be nearly log normal. The skewness (S) and kurtosis (K) of the first derivative are compared with new atmospheric data at much higher Reynolds numbers. Reynolds-number dependence is indicated, in conflict with universal equilibrium theory. A modified theory using fluctuating dissipation predicts that S and K have power-law behavior with turbulent Reynolds number and are related by S ∝ K3/8, in general agreement with the trends of the limited data available.
Citations
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Journal ArticleDOI
TL;DR: In this article, a dynamic renormalization group (RNG) method for hydrodynamic turbulence was developed, which uses dynamic scaling and invariance together with iterated perturbation methods, allowing us to evaluate transport coefficients and transport equations for the large scale (slow) modes.
Abstract: We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumCK=1.617; turbulent Prandtl number for high-Reynolds-number heat transferPt=0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-\(\bar \varepsilon \) model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/\(\bar \varepsilon \), decay of isotropic turbulence asK=O(t−1.3307), and the von Karman constantκ=0.372. A differential transport model, based on differential relations betweenK,\(\bar \varepsilon \), andν, is derived that is not divergent whenK→ 0 and\(\bar \varepsilon \) is finite. This latter model is particularly useful near walls.

3,342 citations

Journal ArticleDOI
TL;DR: In this article, the authors survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, and intermittency models, and the structure and kinematics of small-scale structure.
Abstract: Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

1,183 citations


Cites background from "Measurements of the Small-Scale Str..."

  • ...Data obtained by a number of investigators in the atmosphere (e.g. Gibson et al 1970, Wyngaard & Tennekes 1970, Wyngaard & Pao 1972, Champagne et al 1977, Williams & Paulson 1977, Champagne 1978, Antonia et al 1981, Bradley et al 1985), in laboratory flows (e.g. Antonia et al 1982), and from…...

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Journal ArticleDOI
TL;DR: In this article, the potential of the normal inverse Gaussian distribution and the Levy process for modeling and analysing statistical data, with particular reference to extensive sets of observations from turbulence and from finance, is discussed.
Abstract: The normal inverse Gaussian distribution is defined as a variance-mean mixture of a normal distribution with the inverse Gaussian as the mixing distribution. The distribution determines an homogeneous Levy process, and this process is representable through subordination of Brownian motion by the inverse Gaussian process. The canonical, Levy type, decomposition of the process is determined. As a preparation for developments in the latter part of the paper the connection of the normal inverse Gaussian distribution to the classes of generalized hyperbolic and inverse Gaussian distributions is briefly reviewed. Then a discussion is begun of the potential of the normal inverse Gaussian distribution and Levy process for modelling and analysing statistical data, with particular reference to extensive sets of observations from turbulence and from finance. These areas of application imply a need for extending the inverse Gaussian Levy process so as to accommodate certain, frequently observed, temporal dependence structures. Some extensions, of the stochastic volatility type, are constructed via an observation-driven approach to state space modelling. At the end of the paper generalizations to multivariate settings are indicated.

998 citations


Cites background from "Measurements of the Small-Scale Str..."

  • ...…investigations have shown that the velocity differences typically follow distributions that are close to symmetric and have tails that are either nearly log linear or somewhat heavier than log linear, cf. for instance van Atta & Park (1972), Wyngaard & Tennekes (1970) and Wyngaard & Pao (1972)....

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Journal ArticleDOI
TL;DR: For large enough microscale Reynolds numbers, the data (despite much scatter) support the notion of a "universal" constant that is independent of the flow as well as the Reynolds number, with a numerical value of about 0.5.
Abstract: All known data are collected on the Kolmogorov constant in one‐dimensional spectral formula for the inertial range. For large enough microscale Reynolds numbers, the data (despite much scatter) support the notion of a ‘‘universal’’ constant that is independent of the flow as well as the Reynolds number, with a numerical value of about 0.5. In particular, it is difficult to discern support for a recent claim that the constant is Reynolds number dependent even at high Reynolds numbers.

678 citations

Journal ArticleDOI
TL;DR: In this article, higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and compared with structures in the flow and the equations are forced to maintain steady state turbulence and collect statistics.
Abstract: In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

619 citations

References
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Book
01 Jan 1953
TL;DR: In this article, the kinematics of the field of homogeneous turbulence and the universal equilibrium theory of decay of the energy-containing eddies are discussed. But the authors focus on the dynamics of decay and not on the probability distribution of u(x).
Abstract: Preface 1 Introduction 2 Mathematics representation of the field of turbulence 3 The kinematics of homogeneous turbulence 4 Some linear problems 5 General dynamics of decay 6 The universal equilibrium theory 7 Decay of the energy-containing eddies 8 The probability distribution of u(x) Bibliography of research on homogeneous turbulence Index

3,121 citations