Influence of the wall roughness on a linear shear flow

Abstract

In this paper, we will be interested in the viscous flow fluid over a rough wall which has a periodic roughness and small amplitude. The Reynolds number for the flow over a rough wall is low and the creeping flow equations apply. The no-slip boundary condition on the rough wall applies. By using an asymptotic expansion, the analytic expressions are obtained for the pressure and the components f velocity of the flow of second order due to the roughness, then concluding the expressions of pressure and velocity of the flow on the rough wall.