Unsteady irrotational motion of a fluid around a profile moving between two parallel walls

Using Couchet's (1957) method, a new approximate expression is given for the complex potential for the unsteady irrotational movement of an inviscid incompressible fluid around an arbitrary profile in the presence of a single rectilinear wall. This result is then applied to obtain an approximate complex potential for such motion between two parallel rectilinear walls. A particular case is studied as an example.