Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+ε dimensions

Details Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+ε dimensions Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+ε dimensions

2002-02-22

arxiv.org/abs/nlin/0202049v2

Phys. Rev. Lett., 89 , 064501 (2002)

Nonlinear Sciences

Chaotic Dynamics

PRL, submitted, REVTeX 4, 4 pages

Scientific paper

10.1103/PhysRevLett.89.064501

The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness $\C S \equiv S_3(R)/S^{3/2}_2(R)$ was measured as $\C S_{\text{exp}}\approx 0.03$. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of enstrophy, which exist as true thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We evaluate theoretically the skewness $\C S(d)$ in dimensions ${4/3}\le d\le 2$, show that $\C S(d)=0$ at $d=4/3$, and that it remains as small as $\C S_{\text{exp}}$ in 2-dimensions.

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