  The influence of an axial through-flow on the spatiotemporal growth behavior
of different vortex structures in the Taylor-Couette system with radius ratio
eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the
basic Couette-Poiseuille flow are solved numerically with a shooting method in
a wide range of through-flow strengths Re and different rates of co- and
counterrotating cylinders for toroidally closed vortices with azimuthal wave
number m=0 and for spiral vortex flow with m=+1 and m=-1. For each of these
three different vortex varieties we have investigated (i) axially extended
vortex structures, (ii) axially localized vortex pulses, and (iii) vortex
fronts. The complex dispersion relations of the linearized NSE for vortex modes
with the three different m are evaluated for real axial wave numbers for (i)
and over the plane of complex axial wave numbers for (ii,iii). We have also
determined the Ginzburg-Landau amplitude equation (GLE) approximation in order
to analyze its predictions for the vortex stuctures (ii,iii). Critical
bifurcation thresholds for extended vortex structures are evaluated. The
boundaries between absolute and convective instability of the basic state for
vortex pulses are determined with a saddle-point analysis of the dispersion
relations. Finally, the linearly selected front behavior of growing vortex
structures is investigated. For the two front intensity profiles (increasing in
positive or negative axial direction) 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, -1, respectively.

Fluid Dynamics;Pattern Formation and Solitons