An update on the intermittency exponent in turbulence

Sreenivasan, Katepalli R.; Kailasnath, Purushothaman

doi:10.1063/1.858877

Cited by 154 publications

(141 citation statements)

References 15 publications

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“…In the literature, researchers have reported µ ranging from 0.18 to 0.7. 10,11 In the case of atmospheric data, the 'best' direct estimate is 0.25±0.05 10 and our indirect magnitude cumulant analysis-based result is in agreement with it.…”

Section: A Analysis Of Hot Wire Measurementssupporting

confidence: 78%

“…In this respect, several alternatives (e.g., second-order integral moment, two-point correlation function, spectral density) are available in the literature. [9][10][11] Recently, Cleve et al 12 showed that among various direct approaches, the two-point correlation function ε(x + r)ε(x) of the energy dissipation field provides the most reliable estimates of µ. In this case, one can write ε(x + r)ε(x) ∼ r −µ…”

Section: Introductionmentioning

confidence: 99%

“…Most commonly, fast-response hot wire measurements are used for this purpose. [10][11][12][13][14] However, acquisition of hot wire data in a natural setting could be quite challenging. For example, in the case of atmospheric boundary layer (ABL) field experiments, one needs to perform meticulous hot wire calibration at short regular intervals in order to account for the ever changing (diurnally varying) ABL flow parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating intermittency exponent in neutrally stratified atmospheric surface layer flows: A robust framework based on magnitude cumulant and surrogate analyses

Basu¹,

Foufoula‐Georgiou²,

Lashermes³

et al. 2007

Physics of Fluids

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This study proposes a novel framework based on magnitude cumulant and surrogate analyses to reliably detect and estimate the intermittency coefficient from short-length coarse-resolution turbulent time series. Intermittency coefficients estimated from a large number of neutrally stratified atmospheric surface layer turbulent series from various field campaigns are shown to remarkably concur with well-known laboratory experimental results. In addition, surrogate-based hypothesis testing significantly reduces the likelihood of detecting a spurious non-zero intermittency coefficient from non-intermittent series. The discriminatory power of the proposed framework is promising for addressing the unresolved question of how atmospheric stability affects the intermittency properties of boundary layer turbulence.

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Section: A Analysis Of Hot Wire Measurementssupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimating intermittency exponent in neutrally stratified atmospheric surface layer flows: A robust framework based on magnitude cumulant and surrogate analyses

Basu¹,

Foufoula‐Georgiou²,

Lashermes³

et al. 2007

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…Thus, it is not surprising that numerous studies have been conducted over the past decades for the multiscale characterizations of the ABL wind fields. Diverse methodologies with varying degrees of complexities, ranging from the traditional spectral methods [4][5][6][7][8] to the new-generation multifractal approaches [9][10][11][12][13][14], have been utilized.…”

Section: Introductionmentioning

confidence: 99%

Buoyancy effects on the scaling characteristics of atmospheric boundary-layer wind fields in the mesoscale range

Kiliyanpilakkil¹,

Basu²,

Ruiz-Columbie³

et al. 2015

Phys. Rev. E

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We have analyzed long-term wind speed time-series from five field sites up to a height of 300 m from the ground. Structure function-based scaling analysis has revealed that the scaling exponents in the mesoscale regime systematically depend on height. This anomalous behavior is likely caused by the buoyancy effects. In the framework of the extended self-similarity, the relative scaling exponents portray quasi-universal behavior.

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“…This means that while the β model is not valid quantitatively, it remains valid qualitatively. For experimental works on dissipation correlation and intermittency, see [53][54][55] and more recent [56][57][58][59][60][61].…”

Section: Forced Turbulencementioning

confidence: 99%

Intermittency and local Reynolds number in Navier-Stokes turbulence: A cross-over scale in the Caffarelli-Kohn-Nirenberg integral

Dowker

Ohkitani

2012

Physics of Fluids

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We study space-time integrals which appear in Caffarelli-Kohn-Nirenberg (CKN) theory for the Navier-Stokes equations analytically and numerically. The key quantity is written in standard notations δ(r) = 1/(νr) Qr |∇u| 2 dx dt, which can be regarded as a local Reynolds number over a parabolic cylinder Q r .First, by re-examining the CKN integral we identify a cross-over scale, at which the CKN Reynolds number δ(r) changes its scaling behavior. This reproduces a result on the minimum scale r min in turbulence: r 2 min ∇u ∞ ∝ ν, consistent with a result of Henshaw et al.(1989). For the energy spectrum E(k) ∝ k −q (1 < q < 3), we show that r * ∝ ν a with a = 4 3(3−q) −1. Parametric representations are then obtained as ∇u ∞ ∝ ν −(1+3a)/2 and r min ∝ ν 3(a+1)/4 . By the assumptions of the regularity and finite energy dissipation rate in the inviscid limit, we derive lim p→∞ ζp p = 1 − ζ 2 for any phenomenological models on intermittency, where ζ p is the exponent of p-th order (longitudinal) velocity structure function. It follows that ζ p ≤ (1 − ζ 2 )(p − 3) + 1 for any p ≥ 3 without invoking fractal energy cascade.Second, we determine the scaling behavior of δ(r) in direct numerical simulations of the NavierStokes equations. In isotropic turbulence around R λ ≈ 100 starting from random initial conditions, we have found that δ(r) ∝ r 4 throughout the inertial range. This can be explained by the smallness of a ≈ 0.26, with a result that r * is in the energy-containing range. If the β-model is perfectly correct, the intermittency parameter a must be related to the dissipation correlation exponent µ as µ = 4a 1+a ≈ 0.8 which is larger than the observed µ ≈ 0.20. Furthermore, corresponding integrals are studied using the Burgers vortex and the Burgers equation. In those single-scale phenomena, the cross-over scale lies in the dissipative range. The scale r * offers a practical method of quantifying intermittency. This paper also sorts out a number of existing mathematical bounds and phenomenological models on the basis of the CKN Reynolds number.

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An update on the intermittency exponent in turbulence

Abstract: The issue of experimental determination of the intermittency exponent μ, is revisited and it is shown that the ‘‘best’’ estimate for it is 0.25±0.05. This ‘‘best’’ estimate is obtained from recent atmospheric data, and is based on several different techniques.

Cited by 154 publications

References 15 publications

Estimating intermittency exponent in neutrally stratified atmospheric surface layer flows: A robust framework based on magnitude cumulant and surrogate analyses

Estimating intermittency exponent in neutrally stratified atmospheric surface layer flows: A robust framework based on magnitude cumulant and surrogate analyses

Buoyancy effects on the scaling characteristics of atmospheric boundary-layer wind fields in the mesoscale range

Intermittency and local Reynolds number in Navier-Stokes turbulence: A cross-over scale in the Caffarelli-Kohn-Nirenberg integral

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