Turbulent-Laminar Patterns in Plane Couette Flow

Barkley, Dwight; Tuckerman, Laurette S.

doi:10.1007/1-4020-4049-0_6

Cited by 13 publications

(8 citation statements)

References 27 publications

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“…The cyclic dynamics described in Section 4.1 supports most of the low Reynolds number dynamics observed in this paper. The oscillations described here likely relate to those found in Barkley & Tuckerman (2005) occurring at similar Re and with similar oscillation period. This cyclic dynamics is reminiscent of the self-sustaining process (SSP) (Waleffe 1997(Waleffe , 2009 in which a three-step equilibrium loop was found to support the existence of exact solutions in shear flows.…”

Section: Discussionsupporting

confidence: 71%

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Dynamics of spatially localized states in transitional plane Couette flow

2019

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Section: Discussionsupporting

confidence: 71%

“…The flow dynamics that ensues is long-lived and likely similar to that observed in percolation dynamics (Pomeau 1986;Barkley 2016;Lemoult et al 2016). Chaotic transients have also been observed at such low Reynolds numbers by Schmiegel & Eckhardt (2000) and Barkley & Tuckerman (2005) using different methods.…”

Section: Onset Of Long-lived Chaotic Transientsmentioning

confidence: 54%

Dynamics of spatially localized states in transitional plane Couette flow

2019

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“…In contrast, simulations with a long spanwise length of 120 and a short streamwise length of 10 (corresponding to 0 • ) show repeated nucleation of turbulent regions which persists to Reynolds numbers as low as Re ≈ 200; see Barkley & Tuckerman (2005b).…”

Section: Plane Couette Flow: Turbulent-laminar Banded Patternsmentioning

confidence: 97%

Patterns in Wall-Bounded Shear Flows

Tuckerman

Chantry

Barkley

2020

Annu. Rev. Fluid Mech.

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Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

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“…In an attempt to reduce the computational cost, Barkley & Tuckerman [7,8] chose to consider a long and narrow domain aligned parallel to the wavevector of the periodic modulation of turbulence characterizing the band pattern, usually at the angle with the streamwise direction expected from experiments. So doing, they were able to reproduce most of the pattern's features.…”

Section: Numerical Experiments In Plane Couette Flowmentioning

confidence: 99%

On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

Manneville

2015

European Journal of Mechanics - B/Fluids

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The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re g , the upper bound for unconditional return to the base flow, and the linear instability threshold Re c characterized by unconditional departure from the base flow.The transitional range around Re g is first discussed from an empirical viewpoint ( §1). The recent determination of Re g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re t beyond which turbulence is uniform.Our current theoretical understanding of the problem is next reviewed ( §2): linear theory and nonnormal amplification of perturbations; nonlinear approaches and dynamical systems, basin boundaries and chaotic transients in minimal flow units; spatiotemporal chaos in extended systems and the use of concepts from statistical physics, spatiotemporal intermittency and directed percolation, large deviations and extreme values. Two appendices present some recent personal results obtained in plane Couette flow about patterning from numerical simulations and modeling attempts.Keywords Transition to Turbulence; Pipe Flow; Plane Couette Flow; Laminar-Turbulent Patterning Cautionary note about the literature cited The number of articles related to the topics examined here is tremendous and, though already referring to more than 150 publications, the bibliography is far from exhaustive by at least one order of magnitude. For a better coverage, the reader is invited to consult the literature cited in the review papers mentioned. I tried not to bias the list according to my personal interests, while choosing what I thought to be the most representative papers in each subtopic, sometimes the most recent publications of given people or groups reviewing related works in their introductions and pointing backwards to earlier relevant papers. For convenience, references are listed in alphabetical order of the first author and next chronologically.The article published by O. Reynolds in 1883 [131] founded the scientific approach to the problem of the transition to turbulence. Already an abstract in itself, its title "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels," summarized the main features of the problem and, between the words, identified its control parameter Re nowadays called the Reynolds number. This parameter is a measure of 1 arXiv:1403.6374v1 [physics.flu-dyn]

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Turbulent-Laminar Patterns in Plane Couette Flow

Cited by 13 publications

References 27 publications

Dynamics of spatially localized states in transitional plane Couette flow

Dynamics of spatially localized states in transitional plane Couette flow

Patterns in Wall-Bounded Shear Flows

On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

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