PATTERN SELECTION IN THE ABSOLUTELY UNSTABLE REGIME AS A NONLINEAR EIGENVALUE PROBLEM - TAYLOR VORTICES IN AXIAL-FLOW

A unique pattern selection in the absolutely unstable regime of a driv en, nonlinear, open-flow system is analyzed: The spatiotemporal struct ures of rotationally symmetric vortices that propagate downstream in t he annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial bo undary conditions at the inlet and outlet. Detailed quantitative resul ts for the oscillation frequency, the axial profile of the wave number , and the temporal Fourier amplitudes of the propagating vortex patter ns obtained by numerical simulations of the Navier-Stokes equations ar e compared with results of the appropriate Ginzburg-Landau amplitude e quation approximation and also with experiments. Unlike the stationary patterns in systems without through-flow the spatiotemporal structure s of propagating vortices are independent of parameter history, initia l conditions, and system length. They do, however, depend on the axial boundary conditions in addition to the driving rate of the inner cyli nder and the through-flow rate, Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eige nvalue problem with the frequency being the eigenvalue. The complex am plitude being the corresponding eigenfunction describes the axial stru cture of intensity and wave number. Small, but characteristic differen ces in the structural dynamics between the Navier-Stokes equations and the amplitude equation are mainly due to the different dispersion rel ations. Approaching the border between absolute and convective instabi lity the eigenvalue problem becomes effectively linear and the selecti on mechanism approaches that of linear front propagation.