Two-Loop Calculation of the Anomalous Exponents in the Kazantsev--Kraichnan Model of Magnetic Hydrodynamics

Abstract

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 $\propto \delta (t-t^{\prime })/k^{d+\epsilon }$. 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 ${\epsilon }^2$ of the $\epsilon$ expansion (two-loop approximation).

Presented in the Conference "Mathematical Modeling and Computational Physics" (Stara Lesna, Slovakia, July 2011)

References in corpus (3)

• Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ${\epsilon }^3$
• Anomalous scaling of a passive scalar advected by the Navier--Stokes velocity field: Two-loop approximation
• Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Cited by in corpus (11)

• Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev--Kraichnan kinematic model
• Passive advection of a vector field: Anisotropy, finite correlation time, exact solution and logarithmic corrections to ordinary scaling
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models
• Anomalous scaling in statistical models of passively advected vector fields
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near $d=4$
• Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near $d=4$
• Perspectives on scaling and multiscaling in passive scalar turbulence
• Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture