Fractal Geometric Model for Statistical Intermittency Phenomenon
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 intermitte...
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MDPI AG
2023-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/5/749 |
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| author | Walid Tarraf Diogo Queiros-Condé Patrick Ribeiro Rafik Absi |
| author_facet | Walid Tarraf Diogo Queiros-Condé Patrick Ribeiro Rafik Absi |
| author_sort | Walid Tarraf |
| collection | DOAJ |
| description | 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, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>a</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">γ</mi></mrow><mrow><mi>g</mi><mi>e</mi><mi>o</mi></mrow></msub></mrow></semantics></math></inline-formula>, 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. |
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| last_indexed | 2024-03-11T03:46:17Z |
| publishDate | 2023-05-01 |
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| series | Entropy |
| spelling | doaj.art-fc5c6fc6271e4344852f9c23cfaca03b2023-11-18T01:15:51ZengMDPI AGEntropy1099-43002023-05-0125574910.3390/e25050749Fractal Geometric Model for Statistical Intermittency PhenomenonWalid Tarraf0Diogo Queiros-Condé1Patrick Ribeiro2Rafik Absi3Laboratory of Research in Industrial Eco-Innovation and Energetic (LR2E), Ecole Supérieure d’Ingénieurs ECAM-EPMI, 13 Bd de l’Hautil, 95000 Cergy, FranceLaboratory of Energetics Mechanics and Electromagnetism (LEME), Université Paris Nanterre, Pôle de Ville d’Avray, 50 rue de Sèvres, 92410 Ville d’Avray, FranceLaboratory of Energetics Mechanics and Electromagnetism (LEME), Université Paris Nanterre, Pôle de Ville d’Avray, 50 rue de Sèvres, 92410 Ville d’Avray, FranceLaboratory of Research in Industrial Eco-Innovation and Energetic (LR2E), Ecole Supérieure d’Ingénieurs ECAM-EPMI, 13 Bd de l’Hautil, 95000 Cergy, FranceThe 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, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>a</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">γ</mi></mrow><mrow><mi>g</mi><mi>e</mi><mi>o</mi></mrow></msub></mrow></semantics></math></inline-formula>, 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.https://www.mdpi.com/1099-4300/25/5/749scale entropyentropic skin theoryturbulenceintermittencynonlinear dynamicsstatistical physics |
| spellingShingle | Walid Tarraf Diogo Queiros-Condé Patrick Ribeiro Rafik Absi Fractal Geometric Model for Statistical Intermittency Phenomenon Entropy scale entropy entropic skin theory turbulence intermittency nonlinear dynamics statistical physics |
| title | Fractal Geometric Model for Statistical Intermittency Phenomenon |
| title_full | Fractal Geometric Model for Statistical Intermittency Phenomenon |
| title_fullStr | Fractal Geometric Model for Statistical Intermittency Phenomenon |
| title_full_unstemmed | Fractal Geometric Model for Statistical Intermittency Phenomenon |
| title_short | Fractal Geometric Model for Statistical Intermittency Phenomenon |
| title_sort | fractal geometric model for statistical intermittency phenomenon |
| topic | scale entropy entropic skin theory turbulence intermittency nonlinear dynamics statistical physics |
| url | https://www.mdpi.com/1099-4300/25/5/749 |
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