TY - JOUR

T1 - Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence

AU - Antonov, N. V.

AU - Lanotte, A.

AU - Mazzino, A.

PY - 2000

Y1 - 2000

N2 - 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, δ-correlated in time, and scales with a positive exponent ξ. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to [Formula Presented] 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 [Formula Presented] limit.

AB - 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, δ-correlated in time, and scales with a positive exponent ξ. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with nonuniversal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found nonperturbatively, in any space dimension d, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to [Formula Presented] 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 [Formula Presented] limit.

UR - http://www.scopus.com/inward/record.url?scp=0034206217&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.61.6586

DO - 10.1103/PhysRevE.61.6586

M3 - Article

AN - SCOPUS:0034206217

VL - 61

SP - 6586

EP - 6605

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 6

ER -