Subsonic irrotational inviscid flow around certain bodies with two protruding corners

Abstract

We prove non-existence of nontrivial uniformly subsonic inviscid irrotational flows around several classes of solid bodies with two protruding corners, in particular vertical and angled flat plates; horizontal plates are the only case where solutions exists. This fills the gap between classical results on bodies with a single protruding corner on one hand and recent work on bodies with three or more protruding corners. Thus even with zero viscosity and slip boundary conditions solids can generate vorticity, in the sense of having at least one rotational but no irrotational solutions. Our observation complements the commonly accepted explanation of vorticity generation based on Prandtl's theory of viscous boundary layers.