Periodic solutions and chaos in the Barkley pipe model on a finite domain.

Abstract

Barkley's bipartite pipe model is a continuous two-state reaction-diffusion system that models the transition to turbulence in pipes, and reproduces many qualitative features of puffs and slugs, localized turbulent structures seen during the transition. Extensions to the continuous model, including the incorporation of time delays and constraining the system to finite open domains-a trigger for convective instability-reveal additional solutions to the system, including periodic solutions and chaos unseen in the original 1+1-dimensional system. It is found that the nature of solutions depends strongly on the size of the domain under study as well as choice of boundary conditions: on a finite domain for a particular window of parameter space, period doubling and chaos are observed.