Eckhaus boundary and wave-number selection in rotating Couette-Taylor flow

We present experimental results for the location of the Eckhaus stability boundary in rotating Couette-Taylor flow between concentric cylinders of radius ratios 0. 892 and 0. 747. Generally, they agree well with recent calculations by Riecke and Paap. However, for wave numbers q larger than the critical q₂, the experimental stability boundary lies significantly above the theoretical calculation. We also present experimental results for the wave-number selection by a gentle spatial variation (ramp) of the Reynolds number R from above to below the critical value R₂ for the onset of Taylor-vortex flow. For a sufficiently small ramp angle, the data suggest that a unique, R-dependent value of q is selected, regardless of the aspect ratio (supercritical system length) L. For finite, a band of wave numbers is accessible, and for a given L the system can select one or more discrete values of q within that band. The selected q (L) has a period close to =2/qapeq22. The bandwidth initially decreases as R exceeds R₂, and then increases again. The initial band near R₂ is quantitatively consistent with an explanation offered by Cross. The wave number at high R, although it also has a period of about 2, is phase shifted relative to that near R₂ by half a period. The corresponding stability band and selected q for vanishing have not yet been explained in detail from theory. They are, however, generally consistent with the theoretical considerations of Kramer et al. We also discuss the use of the Ginzburg-Landau equation for estimating R₂ of the infinite system from measurements of the apparent ``onset'' of Taylor-vortex flow in finite systems.