Amplification of Interstellar Magnetic Fields and Turbulent Mixing by Supernova-driven Turbulence. II. The Role of Dynamical Chaos

In this paper we further advance the study of magnetic field amplification in the interstellar medium that we started in 2004. We show that the flux growth rate is comparable to the rate of magnetic energy growth found in the earlier paper. We also demonstrate the role of intermittency in field amplification. The density shows a double-peaked PDF, consistent with the cooling curve that was used. The PDF of the magnetic field shows a high-end tail, providing a telltale signature of the operation of the small-scale dynamo. The magnetic field strength correlates with the density as |B|~(rho)(alpha), with (alpha)= 0.386. As a result, the field amplification takes place more vigorously in the lower temperature, denser gas. The Lagrangian chaos in the simulated turbulent flows is studied in substantial detail. It is shown that the stretching rate of material lines, as well as the Lyapunov exponents, can be used to gain important insights into the growth of magnetic field. The cancellation exponent for the small-scale supernova-driven dynamo is derived, and it is shown that constructive folding of field lines in the dynamo is very inefficient. We also show that our Lagrangian approach can yield actual measures of the turbulent diffusivity in the simulated ISM. The turbulent diffusivity provides insights into the mixing of elements from supernova ejecta on macroscopic scales. The high rates of line stretching in interstellar turbulence suggests that the eventual diffusion of elements at the molecular level is very efficient. Many of the diagnostics of turbulence that are presented here can be used to make direct connections between simulations and observations.