Islands of instability for growth of spiral vortices in the Taylor-Couette system with and without axial through flow

We present numerical calculations of the linearized Navier-Stokes equations for axially extended and axially localized spiral structures in the Taylor-Couette system. The eigenvalue surface for spiral vortices with azimuthal wave number M = 2 shows significantly more structure than that for vortices with M = 0 and 1. Islands are found in parameter space where axially periodic vortex perturbations can grow. Bicriticality of different axial wave numbers is observed. Furthermore, parameter islands of absolute instability are found where wave packets consisting of near-critical extended perturbations can grow and expand via oppositely moving fronts. Some results are compared with those of the Ginzburg-Landau approximation.