Turbulent Mixing in Supernova-Driven Interstellar Turbulence -- The Role of Dynamical Chaos

In this paper we further advance the study of turbulent mixing of supernova ejecta in the interstellar medium that was started in Balsara & Kim (2005, submitted, ApJ). A large set of models for the SN-driven ISM are constructed and several useful observationally parameters are measured from them. Using our models, it is shown that certain choices of magnetic field strength and density do not produce observed values of the rms velocity fluctuations as well as the filling factors for hot gas. As a result, it is shown that our models can help us constrain parameters for the Galactic ISM especially if viable models are taken to be those that reproduce certain observational constraints. 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 nature of turbulent mixing. We also demonstrate the role of intermittency in generating local concentrations of metallicity. 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. Support via NSF grants R36643-7390002, AST-005569-001 and DMS-0204640 is acknowledged.