Laminar-to-Turbulent Transition

Physics: Pipe flow transition is subcritical (hysteretic): turbulence can appear at Re ≈ 2300 but persists down to Re ≈ 1800; no linear instability exists (Orr-Sommerfeld predicts stability for all Re). Bypass transition proceeds via transient growth of streamwise streaks (O(Re) amplification). Turbulent puffs form at Re ~ 2300 (localized, fixed length); slugs form at Re ~ 2700 (growing). Avila et al. (2011) Science: the decay-spreading competition is exactly directed percolation (critical Re ≈ 2040 ± 10).