The characteristic properties of boundary layer and separation in unsteady flow, play a very important role in fluid and structural mechanics because of their drastic effect on control forces generated by aerodynamic surfaces and loads carried by aerodynamic structures.

Prandtl's criterion for separation has been proven experimentally and analytically to be invalid for other than two-dimensional steady flows over fixed walls. Sears and Telionis have proposed a theoretical model for separation for unsteady flow based on the concept of Goldstein's singularity. According to this model a thin layer of reversed flow, embedded within the boundary layer and upstream of separation, may develop in unsteady flows.

In the present study a method is developed to solve numerically the unsteady, two-dimensional, incompressible, boundary-layer equations with arbitrary pressure gradients, capable of integrating through the point of zero skin friction into partially reversed flow and the properties of the boundary layer flow and separation in unsteady flows are studied in detail. In particular the singular behavior of quantities like ∂²u*/∂s∂n, v*, etc. with u*, v* the velocity components and s*, n* the coordinates parallel and perpendicular to the surface of the body, respectively, is investigated and compared with predictions of Goldstein, Moore, Sears and Telionis. The path of zero skin friction and separation singularity with respect to time is also determined. Comparison of the numerical results with existing analytical, numerical and experimental results is made whenever possible. It is believed that the results prove that the point of zero skin friction should not be a downstream limit of the boundary layer calculation in unsteady flow. Further, most of the features of separation predicted by the Sears-Telionis model of unsteady separation are found to be present. Certain characteristic properties of unsteady viscous flow, like vorticity diffusion, steady streaming, etc., are also studied in detail.