Unsteady separation of three-dimensional boundary layers from the Lagrangian viewpoint

Much recent interest centers around the criterion for unsteady separation in the sense of the boundary layer leaving a fixed wall. Available numerical evidence suggests that the boundary layer equation with prescribed pressure distribution would develop at separation a singular behavior analogous to the steady case. We choose to examine the governing equations in Lagrangian description which eliminates the distinction between steady and unsteady flows. Our earlier study for the two-dimensional case reveals that path-line crossing at a given instant is responsible for the appearance of the singularity of the boundary-layer approximation. This idea is extended to the three-dimensional case, and a qualitative explanation of the complex separation patterns over the body surface is presented. For steady flows, our condition lends support to the concept which identifies the envelope of limiting streamlines at the body surface with the 'separation line'