Unsteady laminar separation over impulsively moved cylinders

A numerical method is employed to integrate the unsteady laminar boundary layers about circular and elliptic cylinders started impulsively from rest. An upwind differencing scheme permits the integration through thin layers of reversed flow that are embedded in the boundary layer. The results are in agreement with numerical solutions of the full Navier-Stokes equations and with small time inner-outer expansion solutions. At later times, a singularity of the Goldstein type appears; Sears and Telionis defined this singularity as unsteady boundary-layer separation. For the circular cylinder, this singularity travels upstream and for large times, arrives asymptotically at the point of steady-state separation.