Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev--Kraichnan kinematic model

Abstract

The field theoretic renormalization group and operator product expansion are applied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.

arXiv comment7 pages, LaTeX source. Eqns. (9) and (11) corrected

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• Anomalous scaling in magnetohydrodynamic turbulence: Effects of anisotropy and compressibility in the kinematic approximation
• Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
• Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum
• Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture