Reaction-Diffusion Model Simulations relevant to Modified Taylor-Couette Flow in Systems of Varying Length

Previously, we have observed a period-doubling cascade to chaos in Modified Taylor-Couette Flow with Hourglass Geometry\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).}. Such behavior had been predicted by The Reaction-Diffusion model\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} simulations. The chaotic formation of Taylor-Vortex pair formation was restricted to a very narrow band about the waist of the hourglass. It was suggested that with increasing lengths of systems, the chaotic region would expand. We present a battery of simulations to determine the variation of the size of the chaotic region with length, seeking the transition to spatio- temporal chaos.