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Recently, highly resolved experiments and simulations have provided detailedinsight into the dynamics of turbulent pipe flow. This has revived the interestto identify mechanisms that generate chaotic transients with super-exponentialgrowth of lifetime as a function of a control parameter, the Reynolds numberfor pipe flow, and with transitions from bounded chaotic patches to an invasionof space of irregular motion. Dynamical systems models are unique tools in thisrespect because they can provide insight into the origin of the very long lifetime of puffs, and the dynamical mechanism leading to the transition from puffsto slugs in pipe flow. The present paper contributes to this enterprise byintroducing a unidirectionally coupled map lattice. It mimics three of thesalient features of pipe-flow turbulence: (i) the transition from laminar flowto puffs, (ii) a super-exponential scaling of puff lifetime, and (iii) thetransition from puffs to slugs by an unbinding transition in an intermittencyscenario. In our model all transitions and scalings are theoretically describedfrom a dynamical systems point of view.

Unidirectionally Coupled Map Lattices with Non-Linear Coupling: Unbinding Transitions and Super-Long Transients