Parity-breaking and Hopf bifurcations in axisymmetric Taylor vortex flow

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Abstract
In a linear stability analysis of axisymmetic Taylor vortex flow between counterrotating cylinders we find a parity-breaking bifurcation and a Hopf bifurcation. They are due to an internal resonance of modes with wave number q and 2q and do not break the azimuthal symmetry of the flow. They may lead to drift waves and standing waves, respectively. The standing waves resemble an optical mode, in which adjacent vortex pairs have opposite phase. A temporally periodic driving of the system is expected to excite and stabilize such standing waves. An analysis of the amplitude-phase equations for parity-breaking bifurcations shows that the drift waves can be localized although the parity-breaking bifurcation itself is supercritical. This result applies also to the other systems in which localized drift waves are observed as, for instance, in directional solidification.