J. Phys. II France
Volume 5, Numéro 7, July 1995
Page(s) 1077 - 1092
DOI: 10.1051/jp2:1995231
J. Phys. II France 5 (1995) 1077-1092

Theory of Developed Turbulence: Principle of Maximal Randomness and Spontaneous Parity Violation

L.Ts. Adzhemyan, M. Hnatich and M. Stehlik

Institute of Experimental Physics of Slovak Academy of Sciences, Kosice, CSFR

(Received 21 October 1994, revised 7 March 1995, accepted 5 April 1995)

A set of self-consistent equations in one-loop approximation in a statistical model of fully developed homogeneous isotropic turbulence, which is based on the principle of maximal randomness of the velocity field with a given energy spectral flux, is obtained. These equations do not possess both infrared and ultraviolet divergences near the Kolmogorov values of indices. The formal solution found of the system of equations yields Kolmogorov exponents, but this solution leads to negative Kolmogorov constant $C_{\rm k}$ and negative viscosity. It has been shown, that the turbulent fluid becomes stable if spontaneous parity violation is achieved. Namely, the solution with the Kolmogorov indices and additional helical terms (which lead to positive both $C_{\rm k}$ and effective viscosity) exists. This solution predicts a large, closed to limit value, helical coefficient $\Theta$ in inertial range. The relationship obtained between $C_{\rm k}$ and $\Theta$ confirms this conclusion for the experimental value of $C_{\rm k}$.

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