Information content of turbulence

Cerbus, Rory; Goldburg, W. I.

doi:10.1103/physreve.88.053012

Cited by 38 publications

(28 citation statements)

References 47 publications

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“…Just as with h in Ref. [30], we have found that the general behavior of C and E with respect to Re is independent of the partition size; partitions of sizes A = 4 and 8 gave similar results. Here the choice was made to use the same alphabet size A for all Re.…”

Section: Appendix A: Datasupporting

confidence: 83%

“…All experiments of continuous systems do this because of limited resolution . There are numerous previous studies where even binarizing a turbulent velocity signal has given more insight than traditional techniques [30,[41][42][43].…”

Section: Appendix A: Datamentioning

confidence: 99%

“…(B4), as discussed in Ref. [30] and elsewhere [10,11]. The undersampling bias in the H (U L ) is corrected using Grassberger's method [11], although this did not affect the value of h very much.…”

Section: Appendix B: Entropy Density Hmentioning

confidence: 99%

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Predicting two-dimensional turbulence

Cerbus

Goldburg

2015

Phys. Rev. E

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Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At high Reynolds number, Re, where a cascade exists, turbulence becomes easier to predict as the inertial range broadens. The development of a cascade at low Re is also detected.

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Section: Appendix A: Datasupporting

confidence: 83%

Section: Appendix A: Datamentioning

confidence: 99%

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Predicting two-dimensional turbulence

Cerbus

Goldburg

2015

Phys. Rev. E

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“…Despite the variety of challenges in making accurate measurements, there has been many experiments, observations, and numerical simulations to test the ideas of 2d turbulence theory. For experiments and observations, see the surveys [13,17,45]. One approach is to compare to atmospheric data [19,55], the second approach, convenient for the laboratory setting, is gravity driven soap film channels [16,25,39,44,63,66,67].…”

Section: Introductionmentioning

confidence: 99%

Sufficient Conditions for Dual Cascade Flux Laws in the Stochastic 2d Navier–Stokes Equations

Bedrossian

Zelati

Punshon-Smith

et al. 2020

Arch Rational Mech Anal

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We provide sufficient conditions for mathematically rigorous proofs of the third order universal laws capturing the energy flux to large scales and enstrophy flux to small scales for statistically stationary, forced-dissipated 2d Navier-Stokes equations in the large-box limit. These laws should be regarded as 2d turbulence analogues of the 4/5 law in 3d turbulence, predicting a constant flux of energy and enstrophy (respectively) through the two inertial ranges in the dual cascade of 2d turbulence. Conditions implying only one of the two cascades are also obtained, as well as compactness criteria which show that the provided sufficient conditions are not far from being necessary. The specific goal of the work is to provide the weakest characterizations of the "0-th laws" of 2d turbulence in order to make mathematically rigorous predictions consistent with experimental evidence. Contents2010 Mathematics Subject Classification. 35Q30, 60H30, 76F05.

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“…Up to now, very few research has been devoted to applying IT in the analysis of Turbulent signals [10][11][12][13]. This has probably two main origins.…”

Section: Information Theorymentioning

confidence: 99%

Scaling of information in turbulence

Granero-Belinchon¹,

Roux²,

Garnier³

2016

EPL

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Cf -Entropy in information theory PACS 47.27.Jv -High-Reynolds-number turbulence PACS 89.75.Da -Scaling phenomena in complex systems Abstract -We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to describe the distribution of information amongst scales, and how one can use it to isolate the injection, inertial and dissipative ranges, in perfect agreement with the Batchelor model and with a fractional Brownian motion (fBM) model. We provide analytical derivations of the entropy rate scalings in these two models. In a second stage, we design a conditioning procedure in order to finely probe the asymmetries in the statistics that are responsible for the energy cascade. Our approach is very generic and can be applied to any multiscale complex system.

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Information content of turbulence

Cited by 38 publications

References 47 publications

Predicting two-dimensional turbulence

Predicting two-dimensional turbulence

Sufficient Conditions for Dual Cascade Flux Laws in the Stochastic 2d Navier–Stokes Equations

Scaling of information in turbulence

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