Local and nonlocal magnetic diffusion and alpha-effect tensors in shear flow turbulence

Various approaches to estimate turbulent transport coefficients from numerical simulations of hydromagnetic turbulence are discussed. A quantitative comparison between the averaged magnetic field obtained from a specific three-dimensional simulation of a rotating turbulent shear flow in a slab and a simple one-dimensional alpha-omega dynamo model is given. A direct determination of transport coefficients is attempted by calculating the correlation matrix of different components of the field and its derivatives. The alpha-effect operating on the toroidal field is found to be negative and of similar magnitude as the value obtained previously by correlating the electromotive force with the mean magnetic field. The turbulent diffusion of the toroidal field is comparable to the kinematic viscosity that was determined earlier by comparing the stress with the shear. However, the turbulent diffusion of the radial field component is smaller and can even be formally negative. The method is then modified to obtain the spectral dependence of the turbulent transport coefficients on the wavenumber. There is evidence for nonlocal behavior in that most of the response comes from the smallest wavenumbers corresponding to the largest scale possible in the simulation.