Non-normal and stochastic amplification of magnetic energy in the turbulent dynamo: subcritical case

Mean-field dynamo in a turbulence with shear and kinetic helicity fluctuations

We study the effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau approximation and the second-order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause a large-scale dynamo. A mean-field dynamo is possible when the kinetic helicity fluctuations are inhomogeneous, which causes a nonzero mean alpha effect in a sheared turbulence. On the other hand, the shear-current effect can generate a large-scale magnetic field even in a homogeneous nonhelical turbulence with large-scale shear. This effect was investigated previously for large hydrodynamic and magnetic Reynolds numbers. In this study we examine the threshold required for the shear-current dynamo versus Reynolds number. We demonstrate that there is no need for a developed inertial range in order to maintain the shear-current dynamo (e.g., the threshold in the Reynolds number is of the order of 1).

Stochastic dynamo model for subcritical transition

The effects of stochastic perturbations in a nonlinear alpha Omega-dynamo model are investigated. By using transformation of variables we identify a "slow" variable that determines the global evolution of the non-normal alpha Omega-dynamo system in the subcritical case. We apply an adiabatic elimination procedure to derive a closed stochastic differential equation for the slow variable for which the dynamics is determined along one of the eigenvectors of the full system. We derive the corresponding Fokker-Planck equation and show that the generation of a large scale magnetic field can be regarded as a first-order phase transition. We show that the an advantage of the reduced system is that we have explicit expressions for both the stochastic and deterministic potentials. We also obtain the stationary solution of the Fokker-Planck equation and show that an increase in the intensity of the multiplicative noise leads to qualitative changes in the stationary probability density function. The latter can be interpreted as a noise-induced phase transition. By a numerical simulation of the stochastic galactic dynamo model, we show that the qualitative behavior of the "empirical" stationary pdf of the slow variable is accurately predicted by the stationary pdf of the reduced system.