Rough- and Smooth-Wall Boundary Layer Similarity under Adverse Pressure Gradient Conditions*

Outer layer similarity between rough- and smooth-wall boundary layers is well established for zero pressure gradient flows. Outside the roughness sublayer, which typically extends approximately 3 sand grain roughness heights above the surface, the mean velocity profile, turbulence statistics, and turbulence correlations will match between smooth- and rough-wall cases when quantities are normalized using the boundary layer thickness and the friction velocity u_τ. Recent experiments have shown, however, that if the pressure gradient in terms of the dimensionless acceleration parameter, K=(ν/U_∞²)(dU_∞/dx), is matched between rough- and smooth-wall cases in a non-equilibrium adverse pressure gradient, similarity does not hold. The present work considers whether similarity can be achieved if the Clauser pressure gradient parameter, β=(δ^*/t_o)(dP/dx), history is matched.  Experiments will be conducted in boundary layers on rough and smooth walls with different K distributions to achieve matching β histories. Profiles of mean velocity and turbulence statistics will be measured using a two-component LDV system at multiple streamwise locations and assessed for similarity.