Journal of Fluid Mechanics

Flow regimes in a circular Couette system with independently rotating cylinders

C. David  Andereck a1p1, S. S.  Liu a1p2 and Harry L.  Swinney a1
a1 Department of Physics, The University of Texas, Austin, Texas 78712

Article author query
andereck cd   [Google Scholar] 
liu ss   [Google Scholar] 
swinney hl   [Google Scholar] 


Our flow-visualization and spectral studies of flow between concentric independently rotating cylinders have revealed a surprisingly large variety of different flow states. (The system studied has radius ratio 0.883, aspect ratios ranging from 20 to 48, and the end boundaries were attached to the outer cylinder.) Different states were distinguished by their symmetry under rotation and reflection, by their azimuthal and axial wavenumbers, and by the rotation frequencies of the azimuthal travelling waves. Transitions between states were determined as functions of the inner- and outer-cylinder Reynolds numbers, Ri and Ro, respectively. The transitions were located by fixing Ro and slowly increasing Ri. Observed states include Taylor vortices, wavy vortices, modulated wavy vortices, vortices with wavy outflow boundaries, vortices with wavy inflow boundaries, vortices with flat boundaries and internal waves (twists), laminar spirals, interpenetrating spirals, waves on interpenetrating spirals, spiral turbulence, a flow with intermittent turbulent spots, turbulent Taylor vortices, a turbulent flow with no large-scale features, and various combinations of these flows. Some of these flow states have not been previously described, and even for those states that were previously described the present work provides the first coherent characterization of the states and the transitions between them. These flow states are all stable to small perturbations, and the transition boundaries between the states are reproducible. These observations can serve as a challenge and test for future analytic and numerical studies, and the map of the transitions provides several possible codimension-2 bifurcations that warrant further study.

(Published Online April 21 2006)
(Received December 20 1984)
(Revised September 8 1985)

p1 Present address: Department of Physics, The Ohio State University, Columbus, Ohio 43210.
p2 Present address: Research and Teaching Section of Physics, Department of Basic Sciences, Tianjin University, People's Republic of China.