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Entropy 2017, 19(7), 316;

Laminar-Turbulent Patterning in Transitional Flows

Hydrodynamics Laboratory, CNRS UMR 7646, École Polytechnique, F-91128 Palaiseau, France
Received: 31 May 2017 / Revised: 22 June 2017 / Accepted: 23 June 2017 / Published: 29 June 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
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Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an upper threshold R t above which turbulence is uniform (featureless) and a lower threshold R g below which any form of turbulence decays, possibly at the end of overlong chaotic transients. The most emblematic cases of flow along flat plates transiting to/from turbulence according to this scenario are reviewed. The coexistence is generally in the form of bands, alternatively laminar and turbulent, and oriented obliquely with respect to the general flow direction. The final decay of the bands at R g points to the relevance of directed percolation and criticality in the sense of statistical-physics phase transitions. The nature of the transition at R t where bands form is still somewhat mysterious and does not easily fit the scheme holding for pattern-forming instabilities at increasing control parameter on a laminar background. In contrast, the bands arise at R t out of a uniform turbulent background at a decreasing control parameter. Ingredients of a possible theory of laminar-turbulent patterning are discussed. View Full-Text
Keywords: transition to/from turbulence; wall-bounded shear flow; plane Couette flow; turbulent patterning; phase transitions; directed percolation transition to/from turbulence; wall-bounded shear flow; plane Couette flow; turbulent patterning; phase transitions; directed percolation

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Manneville, P. Laminar-Turbulent Patterning in Transitional Flows. Entropy 2017, 19, 316.

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