Stability and wave-vector restriction of axisymmetric Taylor vortex flow

Abstract

The stability of Taylor vortex flow with respect to axisymmetric perturbations is calculated numerically for several values of the radius ratio. In the nonlinear regime the resulting band of stable wave vectors is considerably smaller than predicted from amplitude expansions. On the low-q side the stability limit departs rather suddenly from the amplitude-expansion result with increasing reduced Reynolds number ${\varepsilon }_R$ and is influenced by the appearance of two bifurcations, which are connected with the coupling of two flows with resonating wave vectors. The influence of these bifurcations becomes stronger with decreasing radius ratio. The wavelength-changing process, however, is still given by the Eckhaus mechanism. The numerical results are in very good agreement with recent quantitative experimental measurements.