Scaling exponents for turbulent velocity and temperature increments

Antonia, R. A.; Pearson, B. R.

doi:10.1209/epl/i1997-00431-5

Cited by 26 publications

(39 citation statements)

References 27 publications

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“…Some groups have plotted v n r ∝ |v r | 3 ξ t n [9,12]. But more recently it has been argued that |v r | n ∝ |u r | 3 ξ t n (45) is theoretically more justified because Kolmogorov's 4/5-law gives an exact prediction for the longitudinal third-order structure function and therefore |u r | 3 is a good point of [16,22,31,59,60].…”

Section: Appendix A: Extended Self-similaritymentioning

confidence: 99%

Joint multi-scale statistics of longitudinal and transversal increments in small-scale wake turbulence

Siefert

Peinke²

2006

Journal of Turbulence

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We analyse the relationship of longitudinal and transversal increment statistics measured in isotropic small-scale turbulence. This is done by means of the theory of Markov processes leading to a phenomenological Fokker-Planck equation for the two increments from which a generalized Kármán equation is derived. We discuss in detail the analysis and show that the estimated equation can describe the statistics of the turbulent cascade. A remarkable result is that the main differences between longitudinal and transversal increments can be explained by a simple rescaling symmetry, namely the cascade speed of the transverse increments is 1.5 times faster than that of the longitudinal increments. Small differences can be found in the skewness and in a higher order intermittency term. The rescaling symmetry is compatible with the Kolmogorov constants and the Kármán equation and gives new insight into the use of extended self-similarity (ESS) for transverse increments. Based on the results we propose an extended self-similarity for the transverse increments (ESST).

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Section: Appendix A: Extended Self-similaritymentioning

confidence: 99%

Joint multi-scale statistics of longitudinal and transversal increments in small-scale wake turbulence

Siefert

Peinke²

2006

Journal of Turbulence

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“…In [8,38,39] the authors plot v n against |u 3 | and obtain that the transverse exponents is smaller than the longitudinal one, ξ n t < ξ n l . In Fig.…”

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confidence: 99%

Different cascade speeds for longitudinal and transverse velocity increments of small-scale turbulence

Siefert

Peinke

2004

Phys. Rev. E

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We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker-Planck equation from which a generalization of the Kármán equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the difference in the scaling properties of these two structure functions.PACS numbers: 47.27. Gs, 47.27.Jv, 05.10.Gg Substantial details of the complex statistical behaviour of fully developed turbulent flows are still unknown, cf. [1,2,3,4]. One important task is to understand intermittency, i.e. finding unexpected frequent occurences of large fluctuations of the local velocity on small length scales. In the last years, the differences of velocity fluctuations in different spatial directions have attracted considerable attention as a main issue of the problem of small scale turbulence, see for example [5,6,7,8,9,10,11,12,13]. For local isotropic turbulence, the statistics of velocity increments [v(x + r) − v(x)] e as a function of the length scale r is of interest. Here, e denotes a unit vector. We denote with u(r) the longitudinal increments (e is parallel to r) and with v(r) transverse increments (e is orthogonal to r) [40].In a first step, this statistics is commonly investigated by means of its moments u n (r) or v n (r) , the so-called velocity structure functions. Different theories and models try to explain the shape of the structure functions cf. [2]. Most of the works examine the scaling of the structure function, u n ∝ r ξ n l , and try to explain intermittency, expressed by ξ n l − n/3 the deviation from Kolmogorov theory of 1941 [14,15]. For the corresponding transverse quantity we write v n ∝ r ξ n t . There is strong evidence that there are fundamental differences in the statistics of the longitudinal increments u(r) and transverse increments v(r). Whereas there were some contradictions initially, there is evidence now that the transverse scaling shows stronger intermittency even for high Reynolds numbers [9,16].A basic equation which relates both quantities is derived by Kármán and Howarth [17]. Assuming incompressibilty and isotropy, the so called first Kármán equation is obtained:Relations between structure functions become more and * Electronic address: peinke@uni-oldenburg.de; URL: http://www.uni-oldenburg.de/hydro more complicated with higher order, including also pressure terms [13,18].In this paper, we focus on a different approach to characterize spatial multipoint correlations via multi-scale statistics. Recently it has been shown that it is possible to get access to the joint probability distribution p(u(r 1 ), u(r 2 ), . . . , u(r n )) via a Fokker-Planck equation, which can be estimated directly from measured data [19,20,21]. For a detailed presentation see [22]. This method is definitely more general than the...

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“…Pioneering (Siggia 1981;Kerr 1985) as well as more recent (Kestener and Arneodo 2003;Kestener 2003;Chen et al 1997a) numerical DNS studies have shown that the enstrophy field is more intermittent than the dissipation field. As suggested by Chen et al (1997b), this difference is likely to result from the difference observed in the scaling exponents f p L and f p T of longitudinal and transverse velocity structure functions, respectively (Malécot et al 2000;Van de Water and Herweijer 1996;Camussi and Benzi 1997;Boratov and Pelz 1997;Grossmann et al 1997;Antonia and Pearson 1997;Dhruva et al 1997). More precisely, Chen et al (1997b) reported numerical results that demonstrate the possible validity of a different RSH for the transverse direction (RSHT) that connects the statistics of the transverse velocity increments to the locally averaged enstrophy in the inertial range.…”

Section: Discussionmentioning

confidence: 98%

“…Actually this estimate is comparable but still slightly larger than the value C 2 . 0.04 extracted from the experimental analysis of transverse velocity increments (Malécot et al 2000;Van de Water and Herweijer 1996;Camussi and Benzi 1997;Boratov and Pelz 1997;Grossmann et al 1997;Antonia and Pearson 1997;Dhruva et al 1997;Chen et al 1997b). Even though one has to be cautious as regard to the rather modest value of R k = 140 of the analyzed DNS data, it is not so surprising that when investigating the full 3D fluctuations of the velocity field, one realizes that this field is much more intermittent than previously estimated from the fluctuations of one of its component only.…”

Section: Velocity Fieldmentioning

confidence: 99%

A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data

Kestener

Arnéodo

2007

Stoch Environ Res Risk Assess

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Extreme atmospheric events are intimately related to the statistics of atmospheric turbulent velocities. These, in turn, exhibit multifractal scaling, which is determining the nature of the asymptotic behavior of velocities, and whose parameter evaluation is therefore of great interest currently. We combine singular value decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued random fields. The so-called Tensorial Wavelet Transform Modulus Maxima (TWTMM) method is calibrated on synthetic self-similar 2D vector-valued multifractal measures and monofractal 3D vector-valued fractional Brownian fields. We report the results of some application of the TWTMM method to turbulent velocity and vorticity fields generated by direct numerical simulations of the incompressible Navier-Stokes equations. This study reveals the existence of an intimate relationship D v ðh þ 1Þ ¼ D x ðhÞ; between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.

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Scaling exponents for turbulent velocity and temperature increments

Cited by 26 publications

References 27 publications

Joint multi-scale statistics of longitudinal and transversal increments in small-scale wake turbulence

Joint multi-scale statistics of longitudinal and transversal increments in small-scale wake turbulence

Different cascade speeds for longitudinal and transverse velocity increments of small-scale turbulence

A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data

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