SYMMETRY-BREAKING BIFURCATIONS FOR THE MAGNETOHYDRODYNAMIC EQUATIONS WITH HELICAL FORCING

We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcin g of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis te chniques have been applied to explore the qualitative behavior of solu tion branches. Due to the symmetry of the forcing, the equations are e quivariant with respect to a group of transformations isomorphic to th e octahedral group, and we have paid special attention to symmetry-bre aking effects. As the Reynolds number is increased, the primary nonmag netic steady state, the ABC flow, loses its stability to a periodic ma gnetic state, showing the appearance of a generic dynamo effect; the c ritical value of the Reynolds number for the instability of the ABC fl ow is decreased compared to the purely hydrodynamic case. The bifurcat ing magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi-periodic branches unt il they end up in chaotic states. In particular detail we have analyze d the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.