Fluctuations of the turbulent diffusion coefficient in galaxy dynamo equations

When studying magnetic fields in galaxies with inhomogeneous media, it is reasonable to study dynamo equations with random coefficients. These equations are useful to describe magnetic fields in galaxies with intensive star formation, supernova explosions and other active processes that change the properties of interstellar media. Before we studied the equations where the alpha-effect coefficient is random. In this paper we study the problem where the turbulent diffusion coefficient has fluctuations. We propose a model where the coefficient takes one of two values with some probabilities on small time intervals and after that renews. We obtain estimates for the asymptotic rates of growth. These estimates are confirmed and improved by numerical simulation procedures. It is shown that for some probabilities the growth of the magnetic field is changed by decay. It is also shown that the intermittency phenomenon takes place in such equations: the higher momenta of the magnetic field grow faster than the lower ones. The magnetic field behavior is studied in the nonlinear case, which corresponds to the appearance of inhomogeneity in the interstellar medium after the instant when the magnetic field has reached the stationary state.