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

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... ce (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. usually the creation of an ensemble of different structure scales, especially small ones, leads to much lower symmetries. On the other hand, in macroscopic models of turbulence (with a cut-off of e.g., high-wavenumber eddies) such assumptions are allowed to be made and, thereby, a virtual higher symmetry may be assumed that leads to simpler results in this limiting case. As a result of all these considerations, a corresponding generalized entropy (see e.g., [2]) for increasing Reynolds number decreases. An increasing stress of a fluid dynamic system is described by an increasing characteristic velocity of the physical system, or in a dimensionless number presentation, by an increasing overall Reynolds number, Re 0 [3]. Therefore, flows with the highest turbulence intensity are occurring when its Reynolds number is infinite. Order in such systems has to do with cooperative behavior, and it usually occurs when a critical value of the external stress is exceeded; in our case this is the critical overall Reynolds number Re 0 c . Other physical systems showing cooperative or critical behavior are magnetic systems, where magnetic moments or spins align (you may think of the aligned hairs in a crew cut of a soldier), defining order in a very obvious manner. Disorder occurs here above a critical temperature, called the Curie temperature, T c , and the order of the system increases if the temperature T is decreased below T c , reaching its maximum at T = 0 K. Egolf et al. solved analytically plane turbulent Couette [4], Poiseuille [5] and "wall" flows [6] by applying a nonlocal and fractional turbulence model [7,8], the Difference-Quotient Turbulence Model (DQTM) (see [9, 10] ). If the continuity and the Navier-Stokes equation (see [11] ) are in a self-similar manner combined with the DQTM, in all these cases a critical phenomenon with a continuous phase transition is revealed (see Figure 1 ). Confirming statements of order-disorder in the work of Egolf et al. 10] ), the stress parameter (for a definition see below) occurs inversely, namely as 1/Re 0 . Thus, one may state that, in analogy to magnetism, the Reynolds number should have been defined inversely or that thermodynamics should be consequently performed by using as its stress parameter the coldness 1/T, instead of the temperature T.