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

Abstract

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 ${q}_{c}$, 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 ${R}_{c}$ for the onset of Taylor-vortex flow. For a sufficiently small ramp angle \ensuremath{\alpha}, the data suggest that a unique, R-dependent value of q is selected, regardless of the aspect ratio (supercritical system length) L. For finite \ensuremath{\alpha}, 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 \ensuremath{\lambda}=2\ensuremath{\pi}/qapeq22. The bandwidth initially decreases as R exceeds ${R}_{c}$, and then increases again. The initial band near ${R}_{c}$ 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 ${R}_{c}$ by half a period. The corresponding stability band and selected q for vanishing \ensuremath{\alpha} 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 ${R}_{c}$ of the infinite system from measurements of the apparent ``onset'' of Taylor-vortex flow in finite systems.