Directed percolation describes lifetime and growth of turbulent puffs and slugs

Abstract

We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1 dimensions fully 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 the main 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.

4 pages, 4 figures. See http://guava.physics.uiuc.edu/projects/Turbulence/dp.html for associated videos

References in corpus (4)

• Directed percolation criticality in turbulent liquid crystals
• Simplifying the complexity of pipe flow
• Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'
• Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

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