Modulated Taylor-Couette flow: Onset of spiral modes

The linear stability of the flow between concentric cylinders, with the inner cylinder rotating at a constant angular velocity and the outer cylinder with an angular velocity varying harmonically about a zero mean, is addressed. The bifurcations of the base state are analyzed using Floquet theory, paying particular attention to non-axisymmetric bifurcations which are dominant in significant regions of parameter space. In these regions the spiral modes of the unforced system become parametrically excited and dominant. This is typical behavior of parametrically forced extended systems, where some modes are stabilized, but others are simultaneously excited. The flow structure of the bifurcated states are examined in detail, paying particular attention to the dynamic implications of their symmetries, and in particular how and when subsequent period doublings are inhibited.