Analysis of localized damping effects in channel flows with a periodic rough boundary

In this study, we justify a modified stationary Navier–Stokes system involving the damping effect for a channel flow with periodic roughness. We solve the modified Navier–Stokes system in a smooth extended channel after reducing the rough boundary to a parameter in a linear damping term. We find that the proposed damping term is valid when the size and amplitude of the imperfection tend to zero. Furthermore, the term yields an quadratic approximation of real flow, i.e. approximation in the -norm, for a small pressure difference. An effective mass flow is also determined up to an order of .