Spiral and Taylor vortex fronts and pulses in axial through flow.

Abstract

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-rotating and counter-rotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with 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) and (iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictions for the vortex structures (ii) and (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. Fit parameters for power-law expansions of the boundaries up to Re4 are listed in two tables. Finally, the linearly selected front behavior of growing vortex structures is investigated using saddle-point analyses of the dispersion relations of NSE and GLE. 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, respectively.