Dynamics of three-tori in a periodically forced Navier-Stokes flow

Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a fini te annular gap between two concentric cylinders, driven by the steady rotat ion and axial harmonic oscillations of the inner cylinder. The three-tori s olutions undergo global bifurcations, including a new gluing bifurcation, a ssociated with homoclinic and heteroclinic connections to unstable solution s (two-tori). These unstable two-tori act as organizing centers for the thr ee-tori dynamics. A discrete space-time symmetry influences the dynamics.