Similarity Between Adverse Pressure Gradient Boundary Layers on Rough and Smooth Walls*

Outside the roughness sublayer, outer layer similarity is observed between canonical zero pressure gradient (ZPG) boundary layers on rough and smooth walls. Profiles of mean velocity and turbulence statistics agree when normalized using the boundary layer thickness and the friction velocity. This similarity allows models developed for smooth wall conditions to be used for flows over rough surfaces, with the roughness effect entering only through the wall boundary condition. New results indicate that similarity holds for adverse pressure gradient (APG) conditions if the Clauser pressure gradient parameter, β=(δ^*/τ_o)(dP/dx), is matched. If the rate of change of β is not too high, the boundary layer can reach a state of near equilibrium, and similarity is observed independent of upstream β history. If the rate of change of β is rapid and/or a departure from equilibrium is caused by the pressure gradient upstream of the APG region, similarity between the rough- and smooth-wall cases can still be achieved if the β history is matched. A dimensionless streamwise coordinate, (xu_τo²)/(δ_oU_eo²) (with δ_o, u_τo, and U_eo the boundary layer thickness, friction velocity and freestream velocity at the start of the APG) is proposed for defining the β history. Experimental results from APG boundary layers with a variety of APG strengths and upstream conditions (e.g. a ZPG or a favorable pressure gradient immediately preceding the APG) will be presented and compared to show the extent of similarity in the mean velocity and Reynolds stresses between rough- and smooth-wall cases.