Imperfect Hopf bifurcation in spiral Poiseuille flow.
We present the results of an experimental study on the transition to spiral vortices in flow between concentric counter-rotating cylinders in the presence of an axial through-flow, i.e., in spiral Poiseuille flow. The experiments were performed in an apparatus having an aspect ratio Gamma=L/d=22.8 ( L axial length, d gap width between cylinders) and end plates enabling an in and outflow of mass. As a result of an applied axial through-flow the "classical" Hopf bifurcation to spiral vortices (SPI) splits up and a primary and secondary branch of down and upstream propagating SPI, respectively, as well as a transient quasiperiodic flow appear. Downstream propagating SPI resulting from the primary supercritical Hopf bifurcation are either convectively or absolutely unstable. The bifurcation structure observed in this open flow experiment is in qualitative agreement with predictions from theory of Hopf bifurcation with broken reflection symmetry [J. D. Crawford and E. Knobloch, Nonlinearity 1, 617 (1988)] and also in quantitative agreement with results from recent numerical calculations [A. Pinter, M. Lücke, and C. Hoffmann, Phys. Rev. E 67, 026318 (2003); C. Hoffmann, M. Lücke, and A. Pinter, Phys. Rev. E 69, 056309 (2004)].
Abshagen
J
J
Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany.
Heise
M
M
Langenberg
J
J
Pfister
G
G