Nonexistence of irrotational flow around solids with protruding corners

Abstract

We motivate and discuss several recent results on non-existence of irrotational inviscid flow around bounded solids that have two or more protruding corners, complementing classical results for the case of a single protruding corner. For a class of two-corner bodies including non-horizontal flat plates, compressible subsonic flows do not exist. Regarding three or more corners, bounded simple polygons do not admit compressible flows with arbitrarily small Mach number, and any incompressible flow has unbounded velocity at at least one corner. Finally, irrotational flow around smooth protruding corners with non-vanishing velocity at infinity does not exist. This can be considered vorticity generating by a slip-condition solid in absence of viscosity.