The phase equation approach for the description of patterns in a spatially varying environment is tested for realistic setups. To this end the phase equation for axisymmetric Taylor vortex flow with spatially varying cylinder radii (spatial ramps) is derived and solved for various geometries which allow a detailed comparison with recent experiments. The wave number selected by subcritical ramps and its dependence on the geometry is determined. A suitable choice of the ramp allows the selection of wave numbers for which the pattern is unstable with respect to a wavelength changing instability (e.g., Eckhaus instability). This leads to a drift of the pattern. The drift velocity is calculated as a function of the Reynolds number for different geometries. Without any adjustable parameters the results for the selected wave numbers as well as for the drift velocities agree well with recent experiments. The calculations suggest the possibility of spatiotemporal chaos in suitably ramped systems.
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