Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as ${\mathrm{SW}}_0$ and ${\mathrm{SW}}_{\pi },$ could be observed. Both modes have an azimuthal wave number $m=1\mathrm{}$ but differ in symmetry. While for ${\mathrm{SW}}_{\pi },$ a spatiotemporal glide-reflection symmetry could be found, ${\mathrm{SW}}_0$ is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The “classical” spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from ${\mathrm{SW}}_0.$ This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.

• Received 26 February 2003

DOI:https://doi.org/10.1103/PhysRevE.68.056308