Directed percolation phase transition to sustained turbulence in Couette flow Journal Article

Author(s): Lemoult, Grégoire; Shi, Liang; Avila, Kerstin; Jalikop, Shreyas V; Avila, Marc; Hof, Björn
Article Title: Directed percolation phase transition to sustained turbulence in Couette flow
Affiliation IST Austria
Abstract: Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature, yet characterizing the transition that gives rise to turbulence in basic shear flows has remained an elusive task. Although, in recent studies, critical points marking the onset of sustained turbulence have been determined for several such flows, the physical nature of the transition could not be fully explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second-order phase transition and falls into the directed percolation universality class. Consequently, the complex laminar–turbulent patterns distinctive for the onset of turbulence in shear flows result from short-range interactions of turbulent domains and are characterized by universal critical exponents. More generally, our study demonstrates that even high-dimensional systems far from equilibrium such as turbulence exhibit universality at onset and that here the collective dynamics obeys simple rules.
Journal Title: Nature Physics
Volume: 12
Issue 3
ISSN: 1745-2473
Publisher: Nature Publishing Group  
Date Published: 2016-02-15
Start Page: 254
End Page: 258
DOI: 10.1038/nphys3675
Notes: We thank P. Maier for providing valuable ideas and supporting us in the technical aspects. Discussions with D. Barkley, Y. Duguet, B. Eckhart, N. Goldenfeld, P. Manneville and K. Takeuchi are gratefully acknowledged. We acknowledge the Deutsche Forschungsgemeinschaft (Project No. FOR 1182), and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589 for financial support. L.S. and B.H. acknowledge research funding by Deutsche Forschungsgemeinschaft (DFG) under Grant No. SFB 963/1 (project A8). Numerical simulations were performed thanks to the CPU time allocations of JUROPA in Juelich Supercomputing Center (project HGU17) and of the Max Planck Computing and Data Facility (Garching, Germany). Excellent technical support from M. Rampp on the hybrid code nsCouette is appreciated.
Open access: no