Influence of Finite-Time Velocity Correlations on Scaling Properties of the Magnetic Field in the Kazantsev-Kraichnan Model: Two-Loop Renormalization Group Analysis

Abstract

Using the field theory renormalization group method and the operator product expansion technique in the two-loop approximation, we investigate the influence of the finite-time correlations of a turbulent velocity field on the anomalous scaling behavior of the single-time two-point correlation functions of the passive magnetic field in the framework of the generalized kinematic Kazantsev-Kraichnan model with the presence of large-scale anisotropy in the three-dimensional case. We briefly discuss the scaling regimes of the model and find two-loop expressions for the anomalous dimensions of the leading composite operators in the operator product expansion as explicit functions of the parameter determining the finite-time correlations of the velocity field in the studied model. We show that the anomalous dimensions of the composite operators near the isotropic shell play a central role in the scaling properties of the model and this allows uniquely determining the two-loop expressions for the scaling exponents of all single-time two-point correlation functions of the magnetic field that drive their scaling properties deep inside the inertial interval. We show that the presence of the finite-time correlations of the velocity field leads to a significantly more pronounced anomalous scaling of the magnetic correlation functions compared with the standard Kazantsev-Kraichnan rapid-change model with the δ-time correlated Gaussian velocity field.