Magnetically induced gluing bifurcations of three-tori in spherical Couette flows

Abstract

The global dynamics of three-tori associated with homoclinic/heteroclinic global (infinite period) bifurcations are investigated for the magnetized spherical Couette problem, a paradigmatic model in geo- and astrophysical magnetohydrodynamics (MHD). A novel homoclinic bifurcation, involving collision between three-tori, is described. In addition, a heteroclinic bifurcation connecting two unstable two-tori with a stable three-torus is also analyzed. The role of the flow's spatial symmetries in this bifurcation scenario is also investigated. This bifurcation scenario gives rise to MHD flows that combine small with extremely large time scales.