Log-similarity for turbulent flows?

Castaing, B.; Gagne, Yves; Marchand, Michel

doi:10.1016/0167-2789(93)90132-k

Cited by 102 publications

(119 citation statements)

References 20 publications

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“…-In (11), we find features already observed in [7]. The generic shape of the velocity and temperature structure functions is not power law (X n and Y n linear in T ), but power-exponential law, as observed and discussed in [1,11,12]. The classical power law shape (or sum of power law shape depending on the way the limit is taken) is obtained in the limit R n → ∞, with T fixed or in the neighborhood of T = 0, with R n fixed:…”

Section: Generic Solution Of Momentsupporting

confidence: 52%

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About Generalized Scaling for Passive Scalars in Fully Developed Turbulence

Dubrulle

1997

J. Phys. II France

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Section: Generic Solution Of Momentsupporting

confidence: 52%

“…Recent studies, however, have raised up doubts about the validity of such scaling: for example, it is shown in [1] that the true scaling could rather be exp(ζ(n)a −1 a ) where a is inversely proportional to the Reynolds number. Given such controversy, the discovery by [2] of a new form of scaling is very interesting.…”

Section: Introductionmentioning

confidence: 99%

About Generalized Scaling for Passive Scalars in Fully Developed Turbulence

Dubrulle

1997

J. Phys. II France

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“…where Cp(j) is the p-th order cumulant of wavelet leaders ℓ(j, k), see the seminal contribution [15]. Estimation.…”

Section: Multifractal Spectrummentioning

confidence: 99%

Hyperspectral image analysis using multifractal attributes

Combrexelle

Wendt

Tourneret

et al. 2015

2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 17041The contribution was presented at WHISPERS 2015 : http://www.ieee-whispers.com/index.php/past-editions/2015-tokyo-japan ABSTRACTThe increasing spatial resolution of hyperspectral remote sensors requires the development of new processing methods capable of combining both spectral and spatial information. In this article, we focus on the spatial component and propose the use of novel multifractal attributes, which extract spatial information in terms of the fluctuations of the local regularity of image amplitudes. The novelty of the proposed approach is twofold. First, unlike previous attempts, we study attributes that efficiently summarize multifractal information in a few parameters. Second, we make use of the most recent developments in multifractal analysis: wavelet leader multifractal formalism, the current theoretical and practical benchmark in multifractal analysis, and a novel Bayesian estimation procedure for one of the central multifractal parameters. Attributes provided by these stateof-the-art multifractal analysis procedures are studied on two sets of hyperspectral images. The experiments suggest that multifractal analysis can provide relevant spatial/textural attributes which can in turn be employed in tasks such as classification or segmentation.

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“…When plotting ln P a (ln|T |) vs ln |T|, one gets the remarkable result that for any scale in the inertial range, all the data points fall on a parabola, which is a strong indication that the statistics of the logarithm of the WT coe cients is deÿnitely Gaussian with a mean and a variance that depend upon the scale parameters [98,105]. This implies that, along the line of Castaing et al ansatz [96,[110][111][112][113][114][115][116], the WTMM pdf at a given scale a can be expressed in terms of the pdf at a coarser scale a as…”

Section: Fully Developed Turbulencementioning

confidence: 99%

Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences

Arnéodo

Audit

Bacry

et al. 1998

Physica A: Statistical Mechanics and its Applications

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We use the continuous wavelet transform to generalize the multifractal formalism to fractal functions. We report the results of recent applications of the so-called wavelet transform modulus maxima (WTMM) method to fully developed turbulence data and DNA sequences. We conclude by brie y describing some works currently under progress, which are likely to be the guidelines for future research. c 1998 Elsevier Science B.V. All rights reserved From global to local characterization of the regularity of fractal functionsIn many situations in physics as well as in some applied sciences, one is faced to the problem of characterizing very irregular functions [1][2][3][4][5][6][7][8][9][10][11]. The examples range from plots of various kinds of random walks, e.g. Brownian signals [12,13], to ÿnancial timeseries [14][15][16], to geological shapes [1,9,17], to medical time-series [18], to interfaces developing in far from equilibrium growth processes [4,6,11], to turbulent velocity signals [10,19,20] and to "DNA walks" coding nucleotide sequences [21,22]. These functions can be qualiÿed as fractal functions [1,13,[23][24][25] whenever their graphs are fractal sets in R 2 (for our purpose here we will only consider functions from R to R). They are commonly called self-a ne functions since their graphs are similar to themselves when transformed by anisotropic dilations, i.e., when shrinking along the x-axis by a factor followed by a rescaling of the increments of the function by a di erent factor −H

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Log-similarity for turbulent flows?

Cited by 102 publications

References 20 publications

About Generalized Scaling for Passive Scalars in Fully Developed Turbulence

About Generalized Scaling for Passive Scalars in Fully Developed Turbulence

Hyperspectral image analysis using multifractal attributes

Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences

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