Anomalous scaling and anisotropy persistence in kinematic magnetohydrodynamic turbulence.

Abstract

The scaling inertial-range behavior of the single-time two-point correlation functions of the weak magnetic field, passively advected by the turbulent velocity field driven by the stochastic Navier-Stokes equation, is investigated in the framework of the field-theoretic renormalization group approach in the second order of the corresponding perturbative expansion (in the two-loop approximation in the language of quantum field theory). The explicit two-loop expressions for the corresponding scaling exponents are found and compared to those obtained in the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the simple Gaussian statistics of the turbulent velocity field. It is shown that, in general, the presence of higher correlations of the velocity field in the turbulent kinematic magnetohydrodynamics leads to more pronounced anomalous scaling behavior of the magnetic correlations deep inside the inertial interval. Moreover, the analysis of the asymptotic behavior of dimensionless ratios of the single-time two-point correlation functions of the magnetic field shows that even the persistence of anisotropy deep inside the inertial range is more pronounced in the genuine kinematic magnetohydrodynamics with the Navier-Stokes turbulent velocity field than in the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the complete absence of higher correlations of the turbulent velocity field.