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The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio η = 0.5 is determined. The Navier we have determined front velocities, axial growth rates, and the wave numbers and frequencies of the unfolding vortex patterns with azimuthal wave numbers m = 0, ±1, respectively.

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, non-rotating end-walls in axial direction. As in the axial periodic case, these transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. But in the presence of rigid lids, pure spiral solutions do not occur but are substituted by primary bifurcating, stable wavy spiral structures (wSPI). Similarly to the periodic system, we found a transition from Taylor vortices to wSPI mediated by so called wavy Taylor vortices (wTVF) and, on the other hand, a transition from wSPI to TVF triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wSPI out of basic Ekman flow.

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counterrotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude-equation approximations. Stable cross-spiral structures with continuously varying content of left- and right-spiral modes are found. They provide a stability transferring connection between the initially stable, axially counterpropagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly farther away from the onset of vortex flow.

Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time-dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio eta=0.5 and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. The existence and spatiotemporal properties of rotating defects, modulated Ekman vortices, and the spiral vortex structures in the bulk are elucidated in quantitative detail.