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24 pages, 7493 KiB

Open AccessArticle

Fractal Geometric Model for Statistical Intermittency Phenomenon

by Walid Tarraf, Diogo Queiros-Condé, Patrick Ribeiro and Rafik Absi

Entropy 2023, 25(5), 749; https://doi.org/10.3390/e25050749 - 3 May 2023

Cited by 3 | Viewed by 2657

The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. To verify its ability to describe intermittency, to this model, we applied the entropic skin theory concept. This allowed us to obtain a conceptual validation. We observed that the intermittency phenomenon in our model was adequately described with the multiscale dynamics proposed by the entropic skin theory, coupling the fluctuation levels that extended between two extremes: the bulk and the crest. We calculated the reversibility efficiency γ with two different methods: statistical and geometrical analyses. Both efficiency values,

γ_{s t a t}

and

γ_{g e o}

, showed equality with a low relative error margin, which actually validated our suggested fractal model for intermittency. In addition, we applied the extended self-similarity (E.S.S.) to the model. This highlighted the intermittency phenomenon as a deviation from the homogeneity assumed by Kolmogorov in turbulence. Full article

(This article belongs to the Special Issue Computational and Statistical Physics Approaches for Complex Systems and Social Phenomena II)

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20 pages, 809 KiB

Open AccessArticle

Entropic-Skins Geometry to Describe Wall Turbulence Intermittency

by Diogo Queiros-Conde, Johan Carlier, Lavinia Grosu and Michel Stanislas

Entropy 2015, 17(4), 2198-2217; https://doi.org/10.3390/e17042198 - 13 Apr 2015

Cited by 3 | Viewed by 5037

Abstract

In order to describe the phenomenon of intermittency in wall turbulence and, more particularly, the behaviour of moments and and intermittency exponents ζ_P with the order p and distance to the wall, we developed a new geometrical framework called “entropic-skins geometry” based on the notion of scale-entropy which is here applied to an experimental database of boundary layer flows. Each moment has its own spatial multi-scale support Ω_p (“skin”). The model assumes the existence of a hierarchy of multi-scale sets Ω_p ranged from the “bulk” to the “crest”. The crest noted characterizes the geometrical support where the most intermittent (the highest) fluctuations in energy dissipation occur; the bulk is the geometrical support for the whole range of fluctuations. The model assumes then the existence of a dynamical flux through the hierarchy of skins. The specific case where skins display a fractal structure is investigated. Bulk fractal dimension and crest dimension are linked by a scale-entropy flux defining a reversibility efficiency (d is the embedding dimension). The model, initially developed for homogeneous and isotropic turbulent flows, is applied here to wall bounded turbulence where intermittency exponents are measured by extended self-similarity. We obtained for intermittency exponents the analytical expression with γ ≈ 0.36 in agreement with experimental results. Full article

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