On the unsteady separated flow past a semi-infinite plate: Exact solution of the Brown and Michael model, scaling, and universality

Two-dimensional unsteady separated flow past a semi-infinite plate is considered. The rolling up of the separated shear layer is modeled by a point vortex, whose time-dependent circulation is predicted by an unsteady Kutta condition. The equation of motion for the starting vortex is derived and solved in closed form for any free-stream condition. A time-dependent scaling that captures the universality of the flow is proposed.