The Mean Field Theories of Magnetism and Turbulence
In the last few decades a series of experiments have revealed that turbulence is a cooperative and critical phenomenon showing a continuous phase change with the critical Reynolds number at its onset. However, the applications of phase transition models, such as the Mean Field Theory (MFT), the Heis...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/11/589 |
| _version_ | 1811305615929114624 |
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| author | Peter W. Egolf Kolumban Hutter |
| author_facet | Peter W. Egolf Kolumban Hutter |
| author_sort | Peter W. Egolf |
| collection | DOAJ |
| description | In the last few decades a series of experiments have revealed that turbulence is a cooperative and critical phenomenon showing a continuous phase change with the critical Reynolds number at its onset. However, the applications of phase transition models, such as the Mean Field Theory (MFT), the Heisenberg model, the XY model, etc. to turbulence, have not been realized so far. Now, in this article, a successful analogy to magnetism is reported, and it is shown that a Mean Field Theory of Turbulence (MFTT) can be built that reveals new results. In analogy to compressibility in fluids and susceptibility in magnetic materials, the vorticibility (the authors of this article propose this new name in analogy to response functions, derived and given names in other fields) of a turbulent flowing fluid is revealed, which is identical to the relative turbulence intensity. By analogy to magnetism, in a natural manner, the Curie Law of Turbulence was discovered. It is clear that the MFTT is a theory describing equilibrium flow systems, whereas for a long time it is known that turbulence is a highly non-equilibrium phenomenon. Nonetheless, as a starting point for the development of thermodynamic models of turbulence, the presented MFTT is very useful to gain physical insight, just as Kraichnan’s turbulent energy spectra of 2-D and 3-D turbulence are, which were developed with equilibrium Boltzmann-Gibbs thermodynamics and only recently have been generalized and adapted to non-equilibrium and intermittent turbulent flow fields. |
| first_indexed | 2024-04-13T08:28:32Z |
| format | Article |
| id | doaj.art-faf566e70f314875a660233f4aa1ed08 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T08:28:32Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-faf566e70f314875a660233f4aa1ed082022-12-22T02:54:20ZengMDPI AGEntropy1099-43002017-11-01191158910.3390/e19110589e19110589The Mean Field Theories of Magnetism and TurbulencePeter W. Egolf0Kolumban Hutter1Thermal Sciences and Engineering Institute, University of Applied Sciences of Western Switzerland, CH-1401 Yverdon-les-Bains, Switzerland℅ Laboratory of Hydraulics, Hydrology and Glaciology, Swiss Federal Institute of Technology, ETH, Hönggerberg IAH 58D, CH-8093 Zurich, SwitzerlandIn the last few decades a series of experiments have revealed that turbulence is a cooperative and critical phenomenon showing a continuous phase change with the critical Reynolds number at its onset. However, the applications of phase transition models, such as the Mean Field Theory (MFT), the Heisenberg model, the XY model, etc. to turbulence, have not been realized so far. Now, in this article, a successful analogy to magnetism is reported, and it is shown that a Mean Field Theory of Turbulence (MFTT) can be built that reveals new results. In analogy to compressibility in fluids and susceptibility in magnetic materials, the vorticibility (the authors of this article propose this new name in analogy to response functions, derived and given names in other fields) of a turbulent flowing fluid is revealed, which is identical to the relative turbulence intensity. By analogy to magnetism, in a natural manner, the Curie Law of Turbulence was discovered. It is clear that the MFTT is a theory describing equilibrium flow systems, whereas for a long time it is known that turbulence is a highly non-equilibrium phenomenon. Nonetheless, as a starting point for the development of thermodynamic models of turbulence, the presented MFTT is very useful to gain physical insight, just as Kraichnan’s turbulent energy spectra of 2-D and 3-D turbulence are, which were developed with equilibrium Boltzmann-Gibbs thermodynamics and only recently have been generalized and adapted to non-equilibrium and intermittent turbulent flow fields.https://www.mdpi.com/1099-4300/19/11/589cooperative phenomenoncritical phenomenonphase transitioncompressibilitysusceptibilityvorticibilitymagnetizationvortizationturbulence intensity |
| spellingShingle | Peter W. Egolf Kolumban Hutter The Mean Field Theories of Magnetism and Turbulence Entropy cooperative phenomenon critical phenomenon phase transition compressibility susceptibility vorticibility magnetization vortization turbulence intensity |
| title | The Mean Field Theories of Magnetism and Turbulence |
| title_full | The Mean Field Theories of Magnetism and Turbulence |
| title_fullStr | The Mean Field Theories of Magnetism and Turbulence |
| title_full_unstemmed | The Mean Field Theories of Magnetism and Turbulence |
| title_short | The Mean Field Theories of Magnetism and Turbulence |
| title_sort | mean field theories of magnetism and turbulence |
| topic | cooperative phenomenon critical phenomenon phase transition compressibility susceptibility vorticibility magnetization vortization turbulence intensity |
| url | https://www.mdpi.com/1099-4300/19/11/589 |
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