Influence of time dependent flows on the threshold of the kinematic dynamo action

A numerical study of the influence of slowly evolving velocity fields in the threshold of the dynamo action is presented. Using experimental time averaged velocity fields, harmonic variations are introduced in a kinematic code in order to characterize the response of the magnetic field to a broad range of frequencies. A critical frequency is found around omega(c) = 200 where a transition is obtained. For large values of the frequency (i.e. smaller periods) the magnetic field can not see the velocity fluctuations and the response of the system corresponds to that of the mean flow. For smaller frequencies, the magnetic field sees the slow evolution of the velocity field, and reduces significatively its growth rates when compared to the mean value. This loss of efficiency is due to the dissipation that appears during the transition between the magnetic eigenvectors corresponding to each one of the velocity fields.