Mean- Field Approximation and a Small Parameter in Turbulence Theory

Details Mean- Field Approximation and a Small Parameter in Turbulence Theory Mean- Field Approximation and a Small Parameter in Turbulence Theory

2000-01-13

arxiv.org/abs/nlin/0001027v2

Nonlinear Sciences

Chaotic Dynamics

25 pages, 1 figure

Scientific paper

10.1103/PhysRevE.63.026307

Numerical and physical experiments on two-dimensional (2d) turbulence show that the differences of transverse components of velocity field are well described by a gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume existence of critical space-dimensionality $d=d_{c}$, at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At $d0$ and $r/L\to 0$ in three-dimensional flows in close agreement with experimental data. In addition, some new exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point pdf of transverse velocity difference in developing as well as in the large-scale stabilized two-dimensional turbulence is a gaussian.

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