Reaction-Diffusion Model Simulations of Varying Lengths Employed to interpret Chaotic Taylor Vortex Formation in Modified Taylor-Couette Flow

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 has been modeled by The Reaction-Diffusion equation\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).}. In the experiment, chaotic formation of Taylor-Vortex pair formation was restricted to a very narrow band about the waist of the hourglass. The calculations of Riecke and Paap suggested that a quadrupling of the length of the system would lead to spatial chaos in the vortex formation. We present a careful recreation of the previous calculation and consider an intermediate length. We demonstrate that doubling the length should be sufficient to observe spatially chaotic behavior.