The Transition from Purely Temporal Chaos to Spatio-Temporal Chaos in the Reaction-Diffusion Model

We apply the Reaction-Diffusion model\footnote{H. Riecke and H.- G. Paap, Europhys. Lett. \textbf{14}, 1235 (1991).} to Taylor- Couette flow with hourglass geometry\footnote{Richard J. Wiener \textit{et al}, Phys. Rev. E \textbf{55}, 5489 (1997).}. Previous authors have reported the model's successful prediction of a period doubling cascade to chaos in this physical system. We present the results of a series of such simulations, varying the length of the system. We report a transition from purely temporal chaotic formation of new pairs of Taylor Vortices at the waist of the hourglass, to spatio-temporal chaos of vortex pair formation across a range of locations. These results inform a program of experiments on physical systems of comparable lengths.