A model for transitional plane Couette flow

Manneville, Paul; Locher, Fabien

doi:10.1016/s1287-4620(00)00113-7

Cited by 9 publications

(15 citation statements)

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“…The no-slip model derived above appears to be slightly more general than the stress-free model initially presented in [20]. The two models have exactly the same structure, apart from the term multiplied by β ′′ which is absent in the stress-free case.…”

Section: Comparison Of Stress-free and No-slip Modelsmentioning

confidence: 77%

“…On the other hand, the direct connection to statistical physics suggested by Pomeau [40] and underlying the abstract spatio-temporal intermittency approach [41] may seem far-off though it takes spatial extension into account in an analogous way. Extending previous work by one of us [20,22], the approach developed here intends to bridge the gap between low and high dimensional systems in a concrete way and with a semi-quantitative ambition.…”

Section: Resultsmentioning

confidence: 97%

“…The free-slip model introduced in [20] and used more extensively in [22] was developed by taking advantage of the fact that trigonometric functions form a closed set under differentiation and multiplication. Perturbations were taken of the form: v ′ = V 1 cos(βy) and 1 {u ′ , w ′ } = 1/2{U 0 , W 0 }+{U 1 , W 1 } sin(βy) with β = π/2 and the derivation of the model was straightforward.…”

Section: The No-slip Model At Lowest Ordermentioning

confidence: 99%

“…In this terminology, the number 2 stands for the full in-plane space dependence (x, z) and the suffix .5 suggestively expresses that the dependence on the third, cross-stream, coordinate y is only partly taken into account through low order truncation. This strategy has been developed previously for easy-to-treat but unphysical stress-free boundary conditions at the plates bounding the flow [20] yielding interesting results but at unrealistically low Reynolds numbers [21,22]. Here we focus on realistic no-slip boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Modeling transitional plane Couette flow

Lagha

Manneville

2007

Eur. Phys. J. B

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The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar flow displays striking similarities with experimental findings.

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Section: Comparison Of Stress-free and No-slip Modelsmentioning

confidence: 77%

Section: Resultsmentioning

confidence: 97%

Section: The No-slip Model At Lowest Ordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling transitional plane Couette flow

Lagha

Manneville

2007

Eur. Phys. J. B

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“…In this work we combine these two extensions to study a 9-PDE extension of the 9-ODE model over spanwise-extended (wide) domains to examine how the flow can spanwise-localise. This 9-PDE model, which restricts the dynamics in 2 spatial directions but fully resolves the remaining spanwise direction, is similar in spirit to previous reduced models which fully resolve 2 spatial directions and use a reduced resolution in the other [19,21,22,38]. If [38] described their model as a…”

Section: Introductionmentioning

confidence: 95%

Localization in a spanwise-extended model of plane Couette flow

Chantry

Kerswell

2015

Phys. Rev. E

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We consider a 9-PDE (1-space and 1-time) model of plane Couette flow in which the degrees of freedom are severely restricted in the streamwise and cross-stream directions to study spanwise localisation in detail. Of the many steady Eckhaus (spanwise modulational) instabilities identified of global steady states, none lead to a localized state. Localized periodic solutions were found instead which arise in saddle node bifurcations in the Reynolds number. These solutions appear global (domain filling) in narrow (small spanwise) domains yet can be smoothly continued out to fully spanwise-localised states in very wide domains. This smooth localisation behaviour, which has also been seen in fully-resolved duct flow (Okino 2011), indicates that an apparently global flow structure needn't have to suffer a modulational instability to localize in wide domains.

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Mean flow of turbulent–laminar patterns in plane Couette flow

Barkley¹,

Tuckerman²

2007

J. Fluid Mech.

122

205

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A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x, y, z) ≈ U0(y) + Uc(y) cos(kz) + Us(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent–laminar patterns in other shear flows – Taylor–Couette, rotor–stator, and plane Poiseuille – are compared.

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A model for transitional plane Couette flow

Cited by 9 publications

References 0 publications

Modeling transitional plane Couette flow

Modeling transitional plane Couette flow

Localization in a spanwise-extended model of plane Couette flow

Mean flow of turbulent–laminar patterns in plane Couette flow

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