Boundary limitation of wave numbers in Taylor-vortex flow

We report experimental results for a boundary-mediated wave-number-adjustment mechanism and for a boundary-limited wave-number band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders, with the inner one rotating at an angular frequency Omega. As observed previously, the Eckhaus instability (a bulk instability) is observed, and limits the stable wave-number band, when the system is terminated axially by two rigid, nonrotating plates. The bandwidth is then of order epsilon(1/2) at small epsilon (epsilon = Omega/Omega(c) - 1), and agrees well with calculations based on the equations of motion over a wide epsilon range. When the cylinder axis is vertical and the upper liquid surface is free (i.e., an air-liquid interface), vortices can be generated or expelled at the flee surface because there the phase of the structure is only weakly Dinned. The band of wave numbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small epsilon the boundary-mediated bandwidth is linear in epsilon. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.