Modified Taylor-Couette Flow in Multiply-Waisted Hourglass Geometries Simulations based upon Reaction-Diffusion Models

The Reaction-Diffusion model \footnote{H. Riecke and H.-G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} predicted a period doubling cascade to chaos in a situation analagous Taylor- Couette flow with hourglass geometry. This cascade to chaos was discovered in the actual fluid flow experiments\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).}. We model Taylor-Couette flow in a cylindrical geometry with multiple waists of super-critical flow connected by regions of barely super-critical flow by corresponding Reaction-Diffusion models. We compare our results to the findings of an ongoing experimental program.