title: Simplifying the complexity of pipe flow.
abstract: Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, which additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular, it captures metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction toward uniform, featureless turbulence.
authors.affiliation: Mathematics Institute, University of Warwick, Coventry, United Kingdom. D.Barkley@warwick.ac.uk
authors.forename: Dwight
authors.initials: D
authors.lastname: Barkley