Effects of spanwise streamline curvature on a spatially developing boundary layer

Direct numerical simulation is performed to study the effects of spanwise curvature on transitioning and turbulent boundary layers. Turbulent transition is induced with an array of resolved cuboids. Spanwise curvature is prescribed using a novel approach with a body force that is applied orthogonally to the bulk flow to curve the mean free-stream streamlines at a set radius. The flows are analysed in a streamline-aligned coordinate system. Although the radius of curvature is large compared with the size of the boundary layer, its effects on the development of the boundary layer are appreciable. The results indicate that spanwise curvature induces a non-uniform mean secondary flow and alters the structure of turbulence within the boundary layer. Analytical expressions for the crossflow are derived in the viscous sublayer and log layer. These alterations are visible as changes in the distribution of the turbulent stresses and alignment of the vortical structures with the mean flow. These modifications are responsible for a misalignment between the Reynolds stress tensor and the velocity gradient tensor, which has important consequences for the validity of the widely used Boussinesq turbulent viscosity hypothesis in Reynolds-averaged Navier–Stokes models. Spanwise curvature was observed to decrease turbulent kinetic energy. These results have important implications on the development of turbulence in general applications, such as the flow over a prolate spheroid.