A Program of Reaction-Diffusion Model Simulations of Modified Taylor-Vortex Flow in Systems of Varying Length*

We seek to inform an experimental program of study of Modified Taylor-Vortex Flow with Hourglass Geometry\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).} in systems of varying lengths. These systems are modeled with Reaction-Diffusion equations.\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} For short systems, the formation of phase slips (corresponding to the formation of new pairs of Taylor-Vortices) occurs in a narrow range of positions near the waist of the hourglass. As the system length increases, the range of positions at which phase slips occur increases sharply, suggesting a transition from purely temporal to spatio-temporal chaos. Details of the simulations will be presented.