Primary and secondary Hopf bifurcations in stratified Taylor Couette flow.

François Caton (1) , Béatrice Janiaud , Emil J. Hopfinger (2)

1 LR - Laboratoire de rhéologie
2 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

Experimental and theoretical results for the axially, stably stratified Taylor-Couette flow are presented. The primary instability is a direct Hopf bifurcation. It leads the system into an oscillatory state of confined internal waves, in good agreement with linear stability analysis. The secondary bifurcation, which leads the system to a pattern of drifting nonaxisymmetric vortices, is a subcritical Hopf bifurcation. This first experimental evidence of a global bifurcation is thought to be generic to dynamical systems with one destabilizing and one stabilizing control parameter.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

François Caton, Béatrice Janiaud, Emil J. Hopfinger. Primary and secondary Hopf bifurcations in stratified Taylor Couette flow.. Physical Review Letters, 1999, 83 (23), pp.4647-4650. ⟨hal-00342028⟩