The flow inside a constant-width wind-tunnel contraction is simulated by solving the Reynolds-Averaged Navier-Stokes equations with an eddy-viscosity turbulence model. The results show the presence of longitudinal vortices near the sidewalls centreline. This confirms a former hypothesis involving the generation of skew-induced longitudinal vorticity within the sidewalls boundary layers. Detailed analysis reveals that the flow structure is influenced by viscous effects in the boundary layers and streamline curvature in the potential flow. Three-dimensional boundary-layer profiles on the contraction sidewall are analysed in the framework of the streamline co-ordinate system and its associated hodographic diagram. The resulting profiles help understand the generation of secondary flows and the associated longitudinal vorticity.