Taylor-Couette Flow with Hourglass Geometry of Varying Lengths Simulated by Reaction-Diffusion

Previously, we have observed chaotic formation of Taylor-Vortex pairs in Modified Taylor- Couette Flow with Hourglass Geometry.\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).} In the experiment, the chaotic formation in a shorter system has been restricted to a narrow band about the waist of the hourglass. Such behavior has been modeled by The Reaction-Diffusion equation,\footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} which has been previously studied, by Riecke and Paap. Their calculation suggested that quadrupling length of the system would lead to spatial chaos in the vortex formation. We present a careful recreation of this result and consider an intermediate length. We demonstrate that doubling the length should be sufficient to observe spatially chaotic behavior.