Abstract
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 maximal randomness principle of the incompressible velocity field with stationary energy spectral flux, is obtained. Thanks to the applied principle the model statistics becomes essentially non Gaussian. The set of equations does not possess the infrared and ultraviolet divergences near the obtained Kolmogorov spectral exponents. The solution of these equations leads to the Kolmogorov exponents, but its amplitude proportional to the Kolmogorov constantC k is negative for Euclidean dimensiond=3. Systematic investigation is made of (inertial) steady state scaling solutions for dimensions 2<d<2.55695,where constantC k (d) becomes positive. Considered in this way, the model stability is discussed in the context of widely studied fractal aspects of turbulence.
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We have greatly benefited from discussions with Dr. Altaisky from JINR Dubna. The authors (M.H. and M.S.) are grateful to D. I. Kazakov and to director D. V. Shirkov for hospitality at the Laboratory of Theoretical Physics, JINR, Dubna.
This work was supported by Fundamental Research Russian Fund, International Scientific Fund (grant R-63000) and by Slovak Grant Agency for Science (grant 2/550/93).
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Adzhemyan, L.T., Hnatich, M., Horvath, M. et al. The maximal randomness principle in d-dimensional turbulence. Czech J Phys 45, 491–502 (1995). https://doi.org/10.1007/BF01691686
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DOI: https://doi.org/10.1007/BF01691686