The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford's solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441-457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441-457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.