Directed percolation describes lifetime and growth of turbulent puffs and slugs.

@article{Sipos2011DirectedPD,
  title={Directed percolation describes lifetime and growth of turbulent puffs and slugs.},
  author={Maksim Sipos and Nigel D Goldenfeld},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={84 3 Pt 2},
  pages={
          035304
        }
}
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… CONTINUE READING

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