Directed percolation describes lifetime and growth of turbulent puffs and slugs

Maksim Sipos, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review


We show that directed percolation (DP) simulations in a pipe geometry in 3+1 dimensions capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into the laminar regions. In a spatiotemporally intermittent state between these two regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP also captures some of the quantitative features of the transition, with a superexponentially diverging characteristic lifetime below the transition. Above the percolation threshold, active (turbulent) clusters expand into the inactive (laminar) phase with a well-defined velocity whose scaling with control parameter (Reynolds number or percolation probability) is consistent with experimental results. Our results provide strong evidence in favor of a conjecture of Pomeau.

Original languageEnglish (US)
Article number035304
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - Sep 29 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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