Weak-inertial flow between two rough surfaces

Abstract

“Oseen–Poiseuille” equations are developed from an asymptotic formulation of the three-dimensional Navier–Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier–Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media.