Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals

We present numerical simulations of closed wavy Taylor vortices and of helicoidal wavy spirals in the Taylor-Couette system. These wavy structures appearing via a secondary bifurcation out of Taylor vortex flow and out of spiral vortex flow, respectively, mediate transitions between Taylor and spiral vortices and vice versa. Structure, dynamics, stability and bifurcation behaviour are investigated in quantitative detail as a function of Reynolds numbers and wave numbers for counter-rotating as well as corotating cylinders. These results are obtained by solving the Navier-Stokes equations subject to axial periodicity for a radius ratio η=0.5 with a combination of a finite differences method and a Galerkin method.