Effective boundary condition for a quasi‐Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition
Francisco J. Suárez‐Grau · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2013
We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ<< ϵ2p‐1/p there is no roughness‐induced effect. In the critical case when δϵ ∼ ϵ2p‐1/p we provide a more accurate effective boundary condition of Navier type. Finally, we also obtain corrector result for the pressure and velocity in every cases.