Non-Gaussian generalization of the Kazantsev-Kraichnan model

Abstract

We consider a natural generalization of the Kazantsev-Kraichnan model for small-scale turbulent dynamo. This generalization takes account of statistical time asymmetry of a turbulent flow, and, thus, allows to describe velocity fields with energy cascade. For three-dimensional velocity field, generalized Kazantsev equation is derived, and evolution of the second order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as $P{r}_m\to \infty$, the growth increment tends to the limit known from the T-exponential (Lagrangian deformation) method. Magnetic field generation is shown to be weaker than that in the Gaussian velocity field for any direction of the energy cascade, and depends essentially on the Prandtl number.

6 figures, 1 table

References in corpus (6)

• Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
• Fluctuation dynamo at finite correlation times and the Kazantsev spectrum
• Magnetic dynamo action in random flows with zero and finite correlation times
• Evolution of localized magnetic field perturbations and the nature of turbulent dynamo
• Kazantsev model in nonhelical 2.5D flows
• No feedback is possible in small-scale turbulent magnetic field

Cited by in corpus (8)

• Probing cluster magnetism with embedded and background radio sources in Planck clusters
• Long-term properties of finite-correlation time isotropic stochastic systems
• Suppression of small-scale dynamo in time irreversible turbulence
• Magnetic energy spectrum produced by turbulent dynamo: effect of time irreversibility
• Lagrangian stochastic integrals of motion in isotropic random flows
• Material surfaces in stochastic flows: integrals of motion and intermittency
• Virtual states and exponential decay in small-scale dynamo
• Small-scale turbulent dynamo for low-Prandtl number fluid: comparison of the theory with results of numerical simulations