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Open AccessArticle

The Mean Field Theories of Magnetism and Turbulence

1
Thermal Sciences and Engineering Institute, University of Applied Sciences of Western Switzerland, CH-1401 Yverdon-les-Bains, Switzerland
2
℅ Laboratory of Hydraulics, Hydrology and Glaciology, Swiss Federal Institute of Technology, ETH, Hönggerberg IAH 58D, CH-8093 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(11), 589; https://doi.org/10.3390/e19110589
Received: 22 September 2017 / Revised: 20 October 2017 / Accepted: 30 October 2017 / Published: 3 November 2017
(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
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. View Full-Text
Keywords: cooperative phenomenon; critical phenomenon; phase transition; compressibility; susceptibility; vorticibility; magnetization; vortization; turbulence intensity cooperative phenomenon; critical phenomenon; phase transition; compressibility; susceptibility; vorticibility; magnetization; vortization; turbulence intensity
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Egolf, P.W.; Hutter, K. The Mean Field Theories of Magnetism and Turbulence. Entropy 2017, 19, 589.

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