FLOW PAST A 2-DIMENSIONAL OR 3-DIMENSIONAL STEEP-EDGED ROUGHNESS

Flow past a single small planar or three-dimensional roughness mounted on a smooth surface is investigated theoretically for various edge st eepnesses, the oncoming planar motion being within a boundary layer or other near-wall shear. Nonlinear edge properties at large Reynolds nu mbers largely control the flow responses at the three-dimensional roug hness wing-tips and the impacts of separation(s), among other features . From analysis and computation, criteria are found for the generation of nonlinear upstream influence, downstream influence and separations , for two-and three-dimensional roughnesses, as well as wing-tip separ ations. In particular, it is predicted that with a severe edge (e.g. a 90 degrees forward-facing step) the ratio of the upstream separation distance over the roughness edge height is a constant times Re-W(1/4) in two dimensions, the constant being approximately 0.142 and the Reyn olds number Re-W being based on the roughness edge height and the inci dent velocity slope at the surface. In three dimensions Re-W is multip lied by sin psi, as expected physically, where psi is the tangent angl e of the roughness planform. The ratio prediction above is very genera l, applying not only for any incident shear flow, but also for any fro nt-edge geometry. Other separation and reattachment properties, extens ions and a comparison with an experiment, are also discussed.