Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary | Zendy

John Fabricius | Zendy; Yulia Koroleva | Zendy; Afonso Fernando Tsandzana | Zendy; Peter Wall | Zendy

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Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary

Author(s) -

John Fabricius,

Yulia Koroleva,

Afonso Fernando Tsandzana,

Peter Wall

Publication year - 2014

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2013.0735

Subject(s) - surface finish , reynolds number , bounded function , limit (mathematics) , flow (mathematics) , stokes flow , mathematics , domain (mathematical analysis) , mathematical analysis , reynolds averaged navier–stokes equations , mechanics , surface roughness , limiting , boundary (topology) , wavelength , geometry , physics , optics , materials science , computational fluid dynamics , thermodynamics , turbulence , mechanical engineering , composite material , engineering

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ϵ and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ= ϵ / μ , three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ϵ and μ .

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