Study of Dynamo Action in Three Dimensional Magnetohydrodynamic Plasma with Arnold-Beltrami-Childress Flow

Abstract: For a three dimensional magnetohydrodynamic (MHD) plasma the dynamo action with ABC flow as initial condition has been studied. The study delineates crucial parameter that gives a transition from coherent nonlinear oscillation to dynamo. Further, for both kinematic and dynamic models at magnetic Prandtl number equal to unity the dynamo action is studied for driven ABC flows. The magnetic resistivity has been chosen at a value where the fast dynamo occurs and the growth rate shows no further variation with the change of magnetic Reynold's number. The exponent of growth of magnetic energy increases, indicating a faster dynamo, if a higher wave number is excited compared to the one with a lower wave number. The result has been found to hold good for both kinematic and externally forced dynamic dynamos where the backreaction of magnetic field on the velocity field is no more negligible. In case of an externally forced dynamic dynamo, the super Alfvenic flows have been found to excite strong dynamos giving rise to the growth of magnetic energy of seven orders of magnitude. The back-reaction of magnetic field on the velocity field through Lorentz force term has been found to affect the dynamics of the velocity field and in turn the dynamics of magnetic field, leading to a saturation, when the dynamo action is very prominent.