Boundary Layer Separation.

The phenomenon of separation is one of the most critical features of the flow of viscous fluids about rigid bodies. In the two-dimensional steady-state case, Prandtls criterion vanishing of skin friction appears to be successful in predicting separation. Numerical integrations have indicated that the boundary-layer equations behave singularly at separation, and Goldstein has suggested analytical formulas describing this situation. Prandtls criterion fails to predict meaningful separation for unsteady problems and this seems to have been mostly unnoticed. A general and formal definition of boundary-layer separation is given, based on the concept of Goldsteins singularity. It is demonstrated how from this definition one can deduce meaningful criteria for the unsteady problem as well as other complicated cases, such as three-dimensional or compressible separation flow. A simple formula is suggested for the component of the velocity in the direction parallel to the wall and it is demonstrated that this is in agreement with Goldsteins results for small distance from separation along the wall. A differential equation is derived from the momentum equation which contains the velocity profile at separation. A few applications are included, demonstrating solutions of this equation, which, in the unsteady case, contains the velocity of the phenomenon of separation too.