Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-01-19
Phys. Rev. E, 61 (2000) 6586
Nonlinear Sciences
Chaotic Dynamics
25 pages Latex, 1 Figure
Scientific paper
10.1103/PhysRevE.61.6586
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, $\delta$-correlated in time, and scales with a positive exponent $\xi$. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with non-universal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found non-perturbatively, in any space dimension $d$, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to $O(\xi)$ using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions : the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness etc.) dramatically increase, thus diverging in the $r\to 0$ limit.
Antonov Nikolaj V.
Lanotte Alessandra
Mazzino Andrea
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