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.

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

References in corpus (1)

• Dynamo effect in the Kraichnan magnetohydrodynamic turbulence

Cited by in corpus (3)

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• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions