Turbulent magnetic Prandtl number and magnetic diffusivity quenching from simulations

Forced turbulence simulations are used to determine the turbulent kinematic viscosity, v(t), from the decay rate of a large scale velocity field. Likewise, the turbulent magnetic diffusivity, eta(t), is determined from the decay of a large scale magnetic field. In the kinematic regime, when the field is weak, the turbulent magnetic Prandtl number, v(t)/eta(t), is about unity. When the field is nonhelical, eta(t) is quenched when magnetic and kinetic energies become comparable. For helical fields the quenching is stronger and can be described by a dynamical quenching formula.