Laminar flow in a unilaterally rough channel

This paper deals with an analytical and experimental investigation of lamin ar sheet flow between a smooth and a rough wall. As such, the material pres ented may be of special interest within the context of hydrodynamic lubrica tion. The dynamic and kinematic properties of the flow are described by a n ewly conceived "reduced Reynolds number", and the two length parameters of, respectively, "relative roughness" and "steepness of roughness". The equat ions of motion are solved by the finite element method for the case of sinu soidal roughness, and corresponding measurements are obtained in a speciall y designed two-dimensional wind-tunnel. Good agreement is found to exist be tween numerical and experimental results. The pattern of streamlines and ve locity profiles reflect the influence of the three similitude parameters an d thereby underline the important role played by surface texture in laminar sheet flow.