  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, that
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, a continuous
transition to sustained turbulence via spatiotemporal intermittency (directed
percolation), and a subsequent increase in turbulence fraction towards uniform,
featureless turbulence.
