Limits of Stability and Irregular Flow Patterns in Wavy Vortex Flow.

We have determined the Reynolds number vs axial wavelength stability curve for five- and six-wave states in the range 1.4R(,c) < R < 9R(,c), where R(,c) corresponds to the onset of Taylor vortex flow in the Couette-Taylor system (with the inner cylinder rotating and the outer cylinder at rest; aspect ratio, 32; radius ratio 0.868). Some measurements are also reported for the three- and four -wave states. At points well within the region bounded by the stability curve, the entire flow pattern has an axial periodicity and an m(,1)-fold rotational symmetry (where m(,1) denotes the number of azimuthal waves), even for aspect ratios as large as 290. However, near a stability boundary the flow loses its axial and azimuthal symmetry; then when a stability boundary is reached, there is a change in the number of waves or the number of vortices or both. We found that some of these transitions were abrupt, while others passed through an intermediate mixed-mode state (where two or more modes competing for stability coexist with one another). Furthermore, near certain stability boundaries we found irregular flow patterns, some of which we observed for as long as 80,000 cylinder periods with no discernible change in the flow pattern. We have also measured the speed of the travelling azimuthal waves as a function of Reynolds number (R), radius ratio of the cylinders ((eta)), axial wavelength ((lamda)), number of azimuthal waves (m(,1)), and the aspect ratio ((GAMMA)). Some measurements were also made at large Reynolds numbers where a second azimuthal wave mode with m(,2) waves appears. The wave speed was found to be a complicated but weak function of (lamda), m(,1), m(,2), and (GAMMA), but a strong function of the radius ratio. At large R the wave speed increases monotonically from 0.14(OMEGA) at (eta) = 0.630 to 0.45(OMEGA) at (eta) = 0.950, where (OMEGA) is the rotation frequency of the inner cylinder.