Unidirectionally Coupled Map Lattices with Nonlinear Coupling: Unbinding Transitions and Superlong Transients

Christian Marschler, Jürgen Vollmer

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Recently, highly resolved experiments and simulations have provided detailed insight into the dynamics of turbulent pipe flow. This has revived the interest in identifying mechanisms that generate chaotic transients with superexponential 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 lifetime 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 superexponential 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.
Original languageEnglish
JournalS I A M Journal on Applied Dynamical Systems
Volume13
Issue number3
Pages (from-to)1137-1151
ISSN1536-0040
DOIs
Publication statusPublished - 2014

Keywords

  • coupled map lattice
  • unidirectional coupling
  • nonlinear coupling
  • intermittency
  • unbinding transition
  • pipe flow
  • turbulence lifetime
  • spreading of turbulence

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