Period-doubling cascade to chaotic phase dynamics in Taylor vortex flow with hourglass geometry

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Abstract
We report on an experimental investigation of a ramp-induced Eckhaus instability, a mechanism which creates a period-doubling cascade to spatiotemporal chaos in a quasi-one-dimensional pattern-forming system. This previously experimentally unexplored mechanism for the generation of chaos involves the phase diffusion of a cellular pattern, resulting from a subcritical spatial ramp. If the subcritical ramp selects an Eckhaus-unstable wave number, diffusion toward this wave number triggers persistent phase slips that create (or destroy) cellular structures. Using a nonlinear phase equation to model ramp-induced Eckhaus instabilities, Riecke and Paap predicted richer-than-periodic dynamics, including spatiotemporal chaos for systems with subcritical ramps satisfying certain general conditions. The specific system that we investigated is a variation of Taylor vortex flow, with the inner cylinder replaced by an hourglass geometry, which satisfies the model conditions for a subcritical ramp that generates chaos. We observed a period-doubling cascade to chaotic phase slips, in qualitative agreement with the predictions of Riecke and Paap.