Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-04-05
Phys. Rev. E64: 046310 (2001)
Nonlinear Sciences
Chaotic Dynamics
37 pages, 4 figures, REVTeX
Scientific paper
10.1103/PhysRevE.64.046310
A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation function is described by an infinite family of scaling exponents, which satisfy exact transcendental equations derived explicitly in d dimensions. The exponents are organized in a hierarchical order according to their degree of anisotropy, with the spectrum unbounded from above and the leading exponent coming from the isotropic sector. For the higher-order structure functions, the anomalous scaling behavior is a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators, whose negative critical dimensions determine the exponents. A close formal resemblance of the model with the stirred NS equation reveals itself in the mixing of operators. Using the RG, the anomalous exponents are calculated in the one-loop approximation for the even structure functions up to the twelfth order.
Adzhemyan Loran Ts.
Antonov Nikolaj V.
Runov Anton V.
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