Directed percolation and puff jamming near the transition to pipe turbulence

The onset of turbulence in pipe flow has defied detailed understanding ever since Reynolds' first observations revealed the spatially-heterogeneous nature of the transition. While recent theoretical studies and experiments in simpler, shear-driven flows suggest that the onset of turbulence is a directed percolation non-equilibrium phase transition, whether these findings are generic and apply also to open or pressure-driven flows is unknown. In pipe flow, the extremely long time scales near the transition make direct observations of critical behavior virtually impossible. Here, we circumvent these limitations by experimentally characterizing all pairwise interactions between localized patches of turbulence ("puffs"), and using these interactions as input to renormalization group and computer simulations of minimal models that extrapolate to long length and time scales. We show that the universality class of the transition is directed percolation, from which emerges a jammed phase of puffs above the critical point. The stronger interactions in the jamming regime enable us to explicitly measure the turbulent fraction and confirm model predictions. Our work shows that directed percolation scaling applies beyond simple closed shear flows, and underscores how statistical mechanics can lead to profound, quantitative and predictive insights on turbulent flows and their phases.