Two-Loop Calculation of the Anomalous Exponents in the Kazantsev-Kraichnan Model of Magnetic Hydrodynamics
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. Field theoretic renormalization group methods are applied to the Kazantsev–Kraichnan model of a passive vector advected by the Gaussian velocity field with zero mean and correlation function ∝ δ(t − t′)/k d + ε . Inertial-range anomalous scaling for the tensor pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain “dangerous” composite operators, whose negative critical dimensions determine the anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order ε 2 of the ε expansion (two-loop approximation).
KeywordsTurbulence Renormalization Group Operator Product Expansion Anomalous Scaling Kraichnan’s Rapid-Change Model
Unable to display preview. Download preview PDF.
- 8.Lanotte, A., Mazzino, A.: Anisotropic non-perturbative zero modes for passively advected magnetic fields. Phys. Rev. 60, R3483 (1996)Google Scholar
- 11.Vasiliev, A.N.: The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics. St. Petersburg Institute of Nuclear Physics, St. Petersburg (1998). English translation: Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
- 12.Zeldovich, Y.B., Ruzmaikin, A.A., Sokoloff, D.D.: Magnetic Fields in Astrophysics. Gordon and Breach, New York (1983)Google Scholar