2000/01/19 by N. V. Antonov, Alessandra S. Lanotte, A. Lanotte +2 · 1 citation
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Anisotropy #Anomaly (physics) #Climate variability and models #Correlation function (quantum field theory) #Dimensionless quantity #Exponent #Fluid Dynamics and Turbulent Flows #Geometry #Isotropy #Magnetic field #Magnetohydrodynamic turbulence #Magnetohydrodynamics #Mathematics #Mechanics #Physics #Quantum mechanics #Scaling #Solar and Space Plasma Dynamics #Statistical physics #Turbulence #cond-mat.dis-nn #nlin.CD #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1103/physreve.61.6586
published as Phys. Rev. E, 61 (2000) 6586 · 25 pages Latex, 1 Figure
arxiv created 2000/01/19 · openalex publication_date 2000/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 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-->0 limit.