Evolution of zero-mean magnetic fields in cellular flows

This paper presents the results of numerical simulations to examine the evolution of a zero-mean magnetic field in a steady cellular flow. In the kinematic model the evolution consists of two phases. In general, the time scale for decay in these two phases are those presented by Rhines and Young [“How rapidly is a passive scalar mixed within closed streamlines,” J. Fluid Mech. 133, 135 (1983)]. However, we show that there is a case for which the magnetic energy does not decay on these time scales. In the dynamic model, the evolution is dependent on the strength of the imposed field. For weak fields, the evolution can be satisfactorily approximated by that for the kinematic model. However, as the field strength is increased the approximation ceases to be valid. For stronger fields, there are three primary phases to the decay. For such fields there is an additional phase, in between those for the kinematic model, where the field decays at the ohmic rate.