M. Golubitsky and W.F. Langford
Pattern formation and bistability in flow between counterrotating cylinders
Physica D32 (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.