  We consider a non-Newtonian fluid flow in a thin domain with thickness
$\eta_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. The
flow is described by the 3D incompressible Navier-Stokes system with a
nonlinear viscosity, being a power of the shear rate (power law) of flow index
$p$, with $9/5\leq p<+\infty$. We consider the limit when the thickness tends
to zero and we prove that the three characteristic regimes for Newtonian fluids
are still valid for non-Newtonian fluids, i.e. Stokes roughness
($\eta_\varepsilon\approx \varepsilon$), Reynolds roughness
($\eta_\varepsilon\ll \varepsilon$) and high-frequency roughness
($\eta_\varepsilon\gg \varepsilon$) regime. Moreover, we obtain different
nonlinear Reynolds type equations in each case.
