Spiral Vortices and Taylor Vortices in the Annulus between Rotating   Cylinders and the Effect of an Axial Flow
  We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavior between spiral vortices with azimuthal wave numbers M=+-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1,0,1 vortex structures are changed by an externally imposed axial through-flow with Reynolds numbers in the range -40 <= Re <= 40. Among others we investigate when left handed or right handed spirals or toroidally closed vortices are preferred. 
Ch. Hoffmann, M. L\"ucke, and A. Pinter