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.

We have conducted a flow-visualization and spectral survey of the flow patterns in a circular Couette system with both cylinders rotating [1]. The ranges of occurrence of previously reported flows and some newly observed flows have been determined as functions of the inner- and outer-cylinder Reynolds numbers (Ri and Ro, respectively) for a system with radius ratio 0.883 and aspect ratio 30 (the upper and lower boundaries were attached to the outer cylinder). The flow transitions were located by fixing Ro and slowly increasing Ri; by decreasing Ri several of these transitions were found to have hysteresis. Pattern velocities have been measured for some cases for flows between both counter- and co-rotating cylinders. For example, the turbulent spiral found between counter-rotating cylinders was found to move at an angular velocity of about 0.5Ωο, independent of Ri, for low outer cylinder speeds (Ωο is the angular velocity of the outer cylinder). The following new flows were found with counter-rotating cylinders: (1) wavy spirals (waves on laminar spiral vortices), (2) modulated wavy vortices (two waves on Taylor vortices) at very low Ri, and (3) V-shaped turbulence (a sometimes long- lived transient state of competing right- and left-handed spiral turbulence). We have also characterized several previously reported flows including spiral turbulence, intermittency, and laminar spiral vortices. The time-dependent flows found for co-rotating cylinders consist of periodic, multiply periodic or nonperiodic waves on Taylor vortices [2]. These flows include wavy-inflow and outflow boundary states, wavelets (both boundaries have waves, but they move at different velocities), twists (rope-like patterns internal to the vortices), and combinations of these. Interestingly, the wavy-inflow and outflow boundary states were found to have an axial periodicity extending over two Taylor vortex pairs, twice the axial wavelength of the usual wavy vortex flow.

Five previously unobserved and unpredicted flows are found to occur in a fluid contained between concentric cylinders with the inner cylinder rotating faster than, but in the same direction as, the outer cylinder. Flow visualization and spectral studies of these flows yield the following descriptions: (1) Twisted Taylor vortices—each Taylor vortex contains from 14 to 30 apparent twists. (2) Wavy inflow boundaries—traveling azimuthal waves appear on the inflow boundary between Tayor vortices. (3) Wavy outflow boundaries—traveling azimuthal waves appear on the outflow boundary between Taylor vortices. (4) Wavelets—small-amplitude traveling azimuthal waves of high wavenumber appear on both inflow and outflow boundaries of the vortices; this flow is distinct from the wavy vortex flows observed with only the inner cylinder rotating. (5) Braided vortices—the vortices appear to wrap around one another in an irregular fashion. The first four flow patterns, produced through quasistatic changes in the inner-cylinder speed with the outer-cylinder speed fixed, can be periodic in the azimuthal and axial directions; in contrast, the braided-vortex pattern, produced through a rapid increase of the inner-cylinder speed with the outer-cylinder speed fixed, has neither axial nor azimuthal periodicity. The power spectra of all five flows contain sharp components. The ranges of cylinder speeds for the occurrence of these flows, and for some cases, the wave speeds and wavenumbers are determined.