Phenomenology of turbulent dynamo growth and saturation

With a nonlocal shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers (Pr-m). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local (Pr-m << 1) or nonlocal (Pr-m >> 1) nature of the energy transfers. In both cases, the magnetic energy grows at a small scale and saturates as an inverse cascade.''