# Subsonic irrotational inviscid flow around certain bodies with two protruding corners

## TL;DR

This paper proves that certain bodies with two protruding corners cannot have nontrivial subsonic irrotational inviscid flows, highlighting conditions where vorticity generation occurs even without viscosity.

## Contribution

It establishes non-existence results for flows around bodies with two protruding corners, filling a gap between classical and recent flow theory results.

## Key findings

- Bodies with two protruding corners do not admit nontrivial irrotational flows.
- Horizontal plates are the only bodies with solutions among those with two protruding corners.
- Vorticity can be generated without viscosity, challenging traditional viscous boundary layer explanations.

## 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.