Effects of Finite Geometry on the Wave Number of Taylor-Vortex Flow

We report measurements of the axial variation of the wave number $q$ of Taylor-vortex flow in a system with aspect ratio $17\lesssim L\lesssim 25$ containing ten vortex pairs between rigid nonrotating ends. Near the critical Reynolds number $R_c$, $q$ is very nonuniform when its average value $\overline{q}$ differs significantly from its critical value $q_c$. For sufficiently small $|\overline{q}-q_c|$, the finite geometry eliminates the Eckhaus instability. Our results agree quantitatively with solutions of the Ginzburg-Landau equation.