Transverse Velocity Structure Functions in Developed Turbulence

Kahalerras, H.; Malécot, Y.; Gagne, Yves

doi:10.1007/978-94-009-0297-8_66

Cited by 20 publications

(26 citation statements)

References 4 publications

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“…The above derivation indicates that it applies equally to both longitudinal and transverse moments. This result, therefore, supports the view expressed in [16], where experimental data is discussed which indicates that the transverse and longitudinal velocity increments do, indeed, have the same global statistics. It also agrees with the known isotropic relations between transverse and longitudinal moments [2] for the cases n = 2 and n = 4.…”

Section: (Aunt) = An[recc(r)]n/3 [Ec~(r)jsupporting

confidence: 89%

“…On the other hand, in [15] results are discussed which show the opposite trend to those described in [ 16], and, in particular, indicate a difference between scaling exponents of a longitudinal and transverse structure functions for higher orders. What this might indicate, not unreasonably, is a limited domain of applicability of approximations based on the Gaussian fixed point for higher order moments.…”

Section: (Aunt) = An[recc(r)]n/3 [Ec~(r)jmentioning

confidence: 63%

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Probability distribution functions for small scale turbulence

Giles

1996

Appl. Sci. Res.

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Abstract. The exact expression for the probability distribution function (pdjO, P(Au~), of a velocity difference AuT, over a distance r, in incompressible fluid turbulence, obtained from the Navier-Stokes equations, is used as a basis for deriving approximate profiles for P (Au~). These approximate forms are deduced from an approximate factorisation of the underlying fimctional probability distribution of the flow field, in which the individual factors capture different physical effects. P(AuT) is represented as the integral, with respect to the spatially averaged dissipation rate e~, of the product of the conditional pdf of Aur given e~, and the pdf of e~. The approximation yields the latter as a log-Poisson pdf, while the conditional pdf is found to be a Gaussian for a transverse increment, and the product of a Gaussian and a cubic polynomial for a longitudinal increment. This approximation is equivalent to the refined similarity hypothesis coupled with the log-Poisson distribution, and it possesses the characteristic features of P(Au~), including symmetric profiles for transverse increments, asymmetric profiles for longitudinal increments, and the development of pronounced non-Gaussian features at small separations. The associated scaling exponents for longitudinal and transverse structure functions are shown to be identical, in this approximation, and to assume the log-Poiss0 n form.

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Section: (Aunt) = An[recc(r)]n/3 [Ec~(r)jsupporting

confidence: 89%

Section: (Aunt) = An[recc(r)]n/3 [Ec~(r)jmentioning

confidence: 63%

Probability distribution functions for small scale turbulence

Giles

1996

Appl. Sci. Res.

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“…30,31 Differences have been observed in their scaling, with some authors reporting greater intermittency for the transverse structure functions, 32 and others the opposite. 33 Hence, initial conditions, methodology (particularly identifying the scaling region), inhomogeneity, Reynolds number, and large scale anisotropy may all impact on the results. In a systematic exploration of these effects on jet flow, it was shown that large-scale anisotropy was the primary control, 34 although differences between the longitudinal and transverse structure functions do not necessarily affect the dynamics of the cascade, which can be shown to belong to the same universality class concerning the hierarchical expression of intermittency despite differences in the exponents.…”

Section: A Structure Function and Multifractal Approachesmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations.

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“…2 ͒ Only recently has it become feasible to calculate reliably other components of velocity structure functions, due to the advances in experimental technology and computer capability. Several experimental studies and DNS [3][4][5][6][7][8][9][10][11][12] have been carried out to determine the TSFs. Most of these results 3,6,7,[9][10][11][12] agree that there exist significant differences between scaling exponents of LSFs and those of TSFs for moment orders higher than three.…”

Section: Introductionmentioning

confidence: 99%

“…The TSFs exhibit more intense intermittency than the LSFs. However, there also exist some different conclusions, 4,5,8 which argue that the differences of scaling exponents in experiments and DNS violate the isotropic constraint and attribute to the effects to finite scaling range. 13 A minimal condition for isotropic turbulence is that the scaling exponents for the second-order LSF and TSF must be the same.…”

Section: Introductionmentioning

confidence: 99%

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

Doolen

Chen

1999

Physics of Fluids

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The longitudinal structure function ͑LSF͒ and the transverse structure function ͑TSF͒ in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

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Transverse Velocity Structure Functions in Developed Turbulence

Cited by 20 publications

References 4 publications

Probability distribution functions for small scale turbulence

Probability distribution functions for small scale turbulence

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

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