The three-dimensional skewed flow around circular cylinders placed on smooth, rough rigid and rough mobile (with scour hole) beds was analyzed in terms of the theories of the three-dimensional turbulent boundary layer (3DTBL). Performance of various cross-flow and near-wall similarity models was evaluated and the effects of roughness and scour hole were discerned. Perry and Joubert's model gave best results among cross-flow models. All near-wall models gave nearly identical results because of the small cross-flow but none gave good results. However, some indications of the near-wall similarity were found. The polar plots were found to be helpful in interpreting the cross-flow behavior, especially the effects of roughness and scour hole on it.