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A unique pattern selection in the absolutely unstable regime of a driven,nonlinear, open-flow system is analyzed: The spatiotemporal structures ofrotationally symmetric vortices that propagate downstream in the annulus of therotating Taylor-Couette system due to an externally imposed axial through-floware investigated for two different axial boundary conditions at the in- andoutlet. Unlike the stationary patterns in systems without through-flow thespatiotemporal structures of propagating vortices are independent of parameterhistory, initial conditions, and system's length. They do, however, depend onthe axial boundary conditions, the driving rate of the inner cylinder and thethrough-flow rate. Our analysis of the amplitude equation shows that thepattern selection can be described by a nonlinear eigenvalue problem with thefrequency being the eigenvalue. Approaching the border between absolute andconvective instability the eigenvalue problem becomes effectively linear andthe selection mechanism approaches that one of linear front propagation.PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow