Suárez Grau, Francisco Javier2024-09-092024-09-092015-040044-2267https://hdl.handle.net/11441/162344We consider the quasi-Newtonian flow in a domain with a periodic rough bottom $\Gamma_\varepsilon$ of period of order the small parameter $\varepsilon$ and amplitude $\delta_\varepsilon$, such that $\delta_\varepsilon\ll \varepsilon$. The flow is described by the 3D incompressible non-newtonian Navier-Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening). Assuming that the fluid satisfies the Navier slip condition on $\Gamma_\varepsilon$ and letting $\varepsilon\to 0$, we obtain three different macroscopic models depending on the magnitude of $\delta_\varepsilon$ with respect to $\varepsilon^{2p-1\over p}$, with $p>2$. In the case $\delta_\ep\gg \varepsilon^{2p-1\over p}$ the effective boundary condition in the limit $\ep=0$ is the no-slip condition, while if $\delta_\ep\ll \varepsilon^{2p-1\over p}$ there is no roughness-induced effect. In the critical case when $\delta_\ep\sim \varepsilon^{2p-1\over p}$ 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.application/pdf22engAn error occurred on the license name.An error occurred getting the license - uri.Quasi-Newtonian fluidNavier boundary conditionRough boundaryinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/zamm.201300160