M. Golubitsky and W.F. Langford
Pattern formation and bistability in flow between counterrotating cylinders
Physica D. 32 (1988) 362-392.
In the Taylor-Couette experiment on fluid flow between counterrotating cylinders, there is a bicritical point where the onset of instabilities to Taylor vortex flow (a steady-state bifurcation) and spiral vortex flow (a Hopf bifurcation) meet. The nonlinear mode interactions near this bicritical point are analyzed, exploiting the role of symmetry in the bifurcation theory, and with emphasis on the relevance to experiments, for a range of radius rations 0.43 < eta < 0.98. The mechanism of the pattern formation is elucidated and several new flow patterns and transitions are predicted, including wavy vortices, bistability, hysteresis, and up to 7 quasiperiodic flows.