Flapping, Falling, and the Unsteady Kutta Condition

The problem of determining the unsteady separated flow of an inviscid fluid around a moving flat plate is considered and solved in two dimensions using a boundary integral representation for the complex conjugate velocity field. The Unsteady Kutta condition, which ensures that the velocity field remains finite everywhere, is imposed rigorously and leads to a range of interesting vortex shedding phenomena. The theory is also extended to include the case of a plate falling under gravity, where the motion of the plate and the surrounding fluid are fully coupled via normal pressure forces.