  One-dimensional models are presented for transitional shear flows. The models
have two variables corresponding to turbulence intensity and mean shear. These
variables evolve according to simple equations based on known properties of
transitional turbulence. The first model considered is for pipe flow. A
previous study modeled turbulence using a chaotic tent map. In the present work
turbulence is modeled instead as multiplicative noise. This model captures the
character of transitional pipe flow and contains metastable puffs, puff
splitting, and slugs. These ideas are extended to a limited model of plane
Couette flow.
