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

TL;DR

This paper introduces a unidirectionally coupled map lattice model that captures key features of turbulent pipe flow, including long-lived chaotic states and transitions from puffs to slugs, providing dynamical systems insights.

Contribution

It presents a novel coupled map lattice model that reproduces turbulent pipe flow phenomena and offers a theoretical dynamical systems explanation for observed transitions.

Findings

Reproduces super-exponential puff lifetime scaling

Models transition from laminar flow to puffs and slugs

Provides dynamical systems explanation for turbulence transitions

Abstract

Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest to identify mechanisms that generate chaotic transients with super-exponential growth of lifetime as a function of a control parameter, the Reynolds number for pipe flow, and with transitions from bounded chaotic patches to an invasion of space of irregular motion. Dynamical systems models are unique tools in this respect because they can provide insight into the origin of the very long life time of puffs, and the dynamical mechanism leading to the transition from puffs to slugs in pipe flow. The present paper contributes to this enterprise by introducing a unidirectionally coupled map lattice. It mimics three of the salient features of pipe-flow turbulence: (i) the transition from laminar flow to puffs, (ii) a super-exponential scaling of puff lifetime, and (iii) the transition from puffs to slugs by an unbinding transition in an intermittency scenario. In our model all transitions and scalings are theoretically described from a dynamical systems point of view.