Directed percolation and puff jamming near the transition to pipe turbulence

• Published in: Nature physics Vol. 20; no. 8; pp. 1339 - 1345
• Main Authors: Lemoult, Grégoire, Mukund, Vasudevan, Shih, Hong-Yan, Linga, Gaute, Mathiesen, Joachim, Goldenfeld, Nigel, Hof, Björn
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.08.2024; Nature Publishing Group
• Subjects: 639/766/189; 639/766/530/2795; Atomic; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; Critical point; Fluid dynamics; Fluid flow; Jamming; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Percolation; Phase transitions; Physics; Physics and Astronomy; Pipe flow; Predictions; Shear flow; Statistical mechanics; Theoretical; Time measurement; Turbulence; Turbulent flow
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/s41567-024-02513-0

The onset of turbulence in pipe flow has defied detailed understanding ever since the first observations of the spatially heterogeneous nature of the transition. Recent theoretical studies and experiments in simpler, shear-driven flows suggest that the onset of turbulence is a directed-percolation non-equilibrium phase transition, but whether these findings are generic and also apply to open or pressure-driven flows is unknown. In pipe flow, the extremely long time scales near the transition make direct observations of critical behaviour virtually impossible. Here we find a technical solution to that limitation and show that the universality class of the transition is directed percolation, from which a jammed phase of puffs emerges above the critical point. Our method is to experimentally characterize all pairwise interactions between localized patches of turbulence puffs and use these interactions as input for renormalization group and computer simulations of minimal models that extrapolate to long length and time scales. The strong 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. The nature of turbulence that occurs when fluids flow in a pipe is still controversial. Now the onset of turbulence in pipe flow has been shown to be a directed-percolation phase transition.