Boundary Behavior of Viscous Fluids: Influence of Wall Roughness and Friction-driven Boundary Conditions

Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka

doi:10.1007/s00205-009-0268-z

Cited by 43 publications

(51 citation statements)

References 20 publications

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“…The results of Section 4 could be extended to viscous fluids. For the particular choice V ε (x) = T ε (x), it would recover the results in [6].…”

Section: Introductionsupporting

confidence: 61%

“…with Ψ ε converging weakly- * to zero in W 1,∞ (ω), the results in [6] imply that the limit boundary condition is…”

Section: Introductionmentioning

confidence: 81%

“…Related to this result, it has been studied in [6] the asymptotic behavior of viscous fluids confined in general rough domains, not necessarily periodic. In the particular case of a domain with a rough bottom described by…”

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

On the Navier boundary condition for viscous fluids in rough domains

Casado–Díaz

Luna-Laynez

Suárez‐Grau

2012

SeMA

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In this paper we review some recent results concerning the study of the asymptotic behavior of viscous fluids in rough domains assuming Navier boundary conditions on the rough boundary. Our main interest is to study the relation between both the adherence and the Navier boundary conditions in the case of a boundary with weak rugosities. We show that the roughness acts on the fluid as a friction term. In particular, if the roughness is sufficiently strong, Navier condition implies adherence condition. This generalizes previous results of other authors.

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“…The results of Section 4 could be extended to viscous fluids. For the particular choice V ε (x) = T ε (x), it would recover the results in [6].…”

Section: Introductionsupporting

confidence: 61%

“…with Ψ ε converging weakly- * to zero in W 1,∞ (ω), the results in [6] imply that the limit boundary condition is…”

Section: Introductionmentioning

confidence: 81%

See 1 more Smart Citation

On the Navier boundary condition for viscous fluids in rough domains

Casado–Díaz

Luna-Laynez

Suárez‐Grau

2012

SeMA

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“…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). A wider consensus exists at the RANS level, calculating bottom friction as the local grain-scale values of the "Reynolds stresses" (Kline et al, 1967;Nezu and Nekagawa, 1993;Keshavarzy and Ball, 1997), which has proven especially relevant for flows in small streams over large asperities (Lawless and Robert, 2001;Nikora et al, 2001;Schmeeckle et al, 2007).…”

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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“…Such conditions have been recently derived from homogenization of rough boundaries, see e.g. [11], [3], [9], [4].…”

Section: Introductionmentioning

confidence: 99%

The Incompressible Navier–Stokes System with Time-Dependent Robin-Type Boundary Conditions

Monniaux

Ouhabaz

2015

J. Math. Fluid Mech.

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We show that the incompressible 3D Navier-Stokes system in a C 1,1 bounded domain or a bounded convex domain Ω with a non penetration condition ν · u = 0 at the boundary ∂Ω together with a time-dependent Robin boundary condition of the type ν × curl u = β(t)u on ∂Ω admits a solution with enough regularity provided the initial condition is small enough in an appropriate functional space.

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Boundary Behavior of Viscous Fluids: Influence of Wall Roughness and Friction-driven Boundary Conditions

Cited by 43 publications

References 20 publications

On the Navier boundary condition for viscous fluids in rough domains

On the Navier boundary condition for viscous fluids in rough domains

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

The Incompressible Navier–Stokes System with Time-Dependent Robin-Type Boundary Conditions

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