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A statistical mechanical phase transition to turbulence in a model shear flow

  • Nigel Goldenfeld (a1)
Abstract

It is becoming increasingly clear that the strong spatial and temporal fluctuations observed in a narrow Reynolds number regime around the laminar–turbulent transition in shear flows can best be understood using the concepts and techniques from a seemingly unrelated discipline – statistical mechanics. During the last few years, a consensus has begun to emerge that these phenomena reflect an underlying non-equilibrium phase transition exhibited by a model of interacting particles on a crystalline lattice, directed percolation, that seems very far from fluid mechanics. Now, Chantry et al. (J. Fluid Mech., vol. 824, 2017, R1) have developed a truncated-mode computation of a model shear flow, capable of simulating systems far larger and longer than any previous study and have for the first time generated enough statistical data that a high-precision test of theory is feasible. The results broadly confirm the theory, extending the class of flows for which the directed percolation scenario holds and removing any remaining doubts that non-equilibrium statistical mechanical critical phenomena can be exhibited by the Navier–Stokes equations.

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Copyright
Corresponding author
Email address for correspondence: nigel@illinois.edu
References
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Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333 (6039), 192196.
Chantry, M., Tuckerman, L. S. & Barkley, D. 2017 Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech. 824, R1.
Chate, H. & Manneville, P. 1987 Transition to turbulence via spatiotemporal intermittency. Phys. Rev. Lett. 58, 112115.
Duguet, Y., Schlatter, P. & Henningson, D. S. 2010 Formation of turbulent patterns near the onset of transition in plane Couette flow. J. Fluid Mech. 650, 119129.
Goldenfeld, N. 1992 Lectures on Phase Transitions and the Renormalization Group. Addison-Wesley.
Hof, B., de Lozar, A., Kuik, D. J. & Westerweel, J. 2008 Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow. Phys. Rev. Lett. 101 (21), 214501.
Kaneko, K. 1984 Period-doubling of kink–antikink patterns, quasiperiodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice. Prog. Theor. Phys. 72 (3), 480486.
Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B. 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254258.
Pomeau, Y. 1986 Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23, 311.
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. A 174, 935982.
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249253.
Shih, H.-Y., Hsieh, T.-L. & Goldenfeld, N. 2016 Ecological collapse and the emergence of travelling waves at the onset of shear turbulence. Nat. Phys. 12, 245248.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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