Wall laws for fluid flows at a boundary with random roughness

Basson, Arnaud; Gérard-Varet, David

doi:10.1002/cpa.20237

Cited by 88 publications

(117 citation statements)

References 19 publications

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“…Note that all these works formulate the roughness using a periodic function (whose amplitude and period are supposed to be small). In a context of more general "roughness" patterns, there exists similar recent results, see [3,15].…”

Section: General Frameworksupporting

confidence: 67%

“…Nevertheless, the ansatz will be different, depending on α. Second, recent works on random roughness, see [3,15], could make us think that our results can be extended to more general cases of roughness. In fact, the construction of our development strongly depends on the behavior of solutions of the Stokes equation on a half-space, whose lower boundary is periodic.…”

Section: General Frameworkmentioning

confidence: 81%

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Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors

Chupin¹,

Martin²

2012

SIAM J. Math. Anal.

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We derive the thin film approximation including roughness-induced correctors. This corresponds to the description of a confined Stokes flow whose thickness is of order ε ≪ 1; but we also take into account the roughness patterns of the boundary that are described at order ε 2 , leading to a perturbation of the classical Reynolds approximation. The asymptotic expansion leading to the description of the scale effects is rigorously derived, through a sequence of Reynolds-type problems and Stokes-type boundary layer problems. Well-posedness of the related problems and estimates in suitable functional spaces are proven, at any order of the expansion. In particular, we show that the micro-/macro-scale coupling effects may be analyzed as the consequence of two features: the interaction between the macroscopic scale (order 1) of the flow and the microscopic scale (order ε) is perturbed by the interaction with a microscopic scale of order ε 2 related to the roughness patterns. Moreover, the converging-diverging profile of the confined flow, which is typical in lubrication theory provides additional micro-macro-scales coupling effects. * This work was supported by the ANR project ANR-08-JCJC-0104-01 : RUGO (Analyse et calcul des effets de rugosités sur lesécoulements). The authors are very grateful to David Gérard-Varet for fruitful discussions on the subject of this paper.

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Section: General Frameworksupporting

confidence: 67%

Section: General Frameworkmentioning

confidence: 81%

Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors

Chupin¹,

Martin²

2012

SIAM J. Math. Anal.

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“…In a recent article Basson and Gérard-Varet [4] derive approximate boundary condition for a boundary with random roughness. The analysis of these previous papers is essentially based on the construction of the so-called "wall law", which is a boundary condition imposed on an artificial boundary inside the domain.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Approximate transmission conditions through a rough thin layer: The case of periodic roughness

Ciuperca

Jai

Poignard³

2009

Eur. J. Appl. Math

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Abstract:We study the behavior of the steady-state voltage potentials in a material composed by a bidimensional medium surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be ε-periodic, ε beeing the small thickness of the layer. We build approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends previous works [8,7] of the third author, in which the layer had constant or weakly oscillating thickness.

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“…In the literature, the modelling choices to account for friction phenomena are most often correlated with the refinement of the flow models used (NS, RANS, SV, ASV), but are also constrained by bed topographies and flow typologies in numerous cases. Several studies at the NS level of refinement advocate the use of the "partial slip" (Navier, 1827) condition or related formulations in which the near-bed slip velocity is either proportional to the shear stress (Jäger and Mikelic, 2001;Basson and Gerard-Varet, 2008) or depends on it in a non-linear way (Achdou et al, 1998;Jäger and Mikelic, 2003). Other works plead for "no-slip" conditions (Panton, 1984;CasadoDiaz et al, 2003;Myers, 2003;Bucur et al, 2008Bucur et al, , 2010 or suggest the separation of flow domains within or outside bed asperities, with a complete slip condition (non-zero tangential velocity) at the interface (Gerard-Varet and Masmoudi, 2010).…”

Section: Flow Typology 321 From Friction Laws and Bed Topography Tomentioning

confidence: 99%

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

Cheviron

Moussa²

2016

Hydrol. Earth Syst. Sci.

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Abstract. This review paper investigates the determinants of modelling choices, for numerous applications of 1-D freesurface flow and morphodynamic equations in hydrology and hydraulics, across multiple spatiotemporal scales. We aim to characterize each case study by its signature composed of model refinement (Navier-Stokes: NS; Reynolds-averaged Navier-Stokes: RANS; Saint-Venant: SV; or approximations to Saint-Venant: ASV), spatiotemporal scales and subscales (domain length: L from 1 cm to 1000 km; temporal scale: T from 1 s to 1 year; flow depth: H from 1 mm to 10 m; spatial step for modelling: δL; temporal step: δT ), flow typology (Overland: O; High gradient: Hg; Bedforms: B; Fluvial: F), and dimensionless numbers (dimensionless time period T * , Reynolds number Re, Froude number Fr, slope S, inundation ratio z , Shields number θ ). The determinants of modelling choices are therefore sought in the interplay between flow characteristics and cross-scale and scale-independent views. The influence of spatiotemporal scales on modelling choices is first quantified through the expected correlation between increasing scales and decreasing model refinements (though modelling objectives also show through the chosen spatial and temporal subscales). Then flow typology appears a secondary but important determinant in the choice of model refinement. This finding is confirmed by the discriminating values of several dimensionless numbers, which prove preferential associations between model refinements and flow typologies. This review is intended to help modellers in positioning their choices with respect to the most frequent practices, within a generic, normative procedure possibly enriched by the community for a larger, comprehensive and updated image of modelling strategies.

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Wall laws for fluid flows at a boundary with random roughness

Cited by 88 publications

References 19 publications

Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors

Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors

Approximate transmission conditions through a rough thin layer: The case of periodic roughness

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

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