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Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence | N.V. Antonov
; A. Lanotte
; A. Mazzino
; | Date: |
19 Dec 1999 | Journal: | Phys. Rev. E, 61 (2000) 6586 | Subject: | Chaotic Dynamics; Fluid Dynamics; Plasma Physics; Disordered Systems and Neural Networks | nlin.CD cond-mat.dis-nn physics.flu-dyn physics.plasm-ph | Abstract: | 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 $r o 0$ limit. | Source: | arXiv, nlin.CD/0001039 | Services: | Forum | Review | PDF | Favorites |
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