  The flow of viscous incompressible fluid over a periodically corrugated
surface is investigated numerically by solving the Navier-Stokes equation with
the local slip and no-slip boundary conditions. We consider the effective slip
length which is defined with respect to the level of the mean height of the
surface roughness. With increasing corrugation amplitude the effective no-slip
boundary plane is shifted towards the bulk of the fluid, which implies a
negative effective slip length. The analysis of the wall shear stress indicates
that a flow circulation is developed in the grooves of the rough surface
provided that the local boundary condition is no-slip. By applying a local slip
boundary condition, the center of the vortex is displaced towards the bottom
the grooves and the effective slip length increases. When the intrinsic slip
length is larger than the corrugation amplitude, the flow streamlines near the
surface are deformed to follow the boundary curvature, the vortex vanishes, and
the effective slip length saturates to a constant value. Inertial effects
promote vortex flow formation in the grooves and reduce the effective slip
length.
