This article reports on an experimental study of turbulent flows over periodic arrays of transverse square ribs attached to the bottom and top walls of an asymmetric converging channel preceded by an upstream parallel section. In the first and second series of experiments, the ribs on both walls were, respectively, arranged perpendicular and then at an angle of 45 degrees to the sidewalls of the channel in a non-staggered configuration. A high-resolution particle image velocimetry system was used to conduct detailed velocity measurements in the upstream parallel and converging sections of the channel. For the 45 degrees ribs, measurements were made at three different streamwise planes to capture the secondary motions produced by the inclined ribs. From these measurements, profiles and contours of the mean velocities, one-point turbulent statistics including the Reynolds stresses, Reynolds stress ratios, triple velocity correlations, and two-point correlation functions were obtained. These results, together with reference smooth-wall measurements in the fully developed section of a plane channel, are used to document the effects of rib roughness, pressure gradient, rib inclination, and spanwise location of the mean flow and turbulent statistics.