Piecewise analytic bodies in subsonic potential flow

TL;DR

This paper proves the nonexistence of certain subsonic potential flows around bodies with multiple protruding corners and shows velocity unboundedness in incompressible flows, extending previous results to more general cases.

Contribution

It generalizes earlier low-Mach limit results to bodies with three or more protruding corners and establishes velocity unboundedness in incompressible flows.

Findings

No nonzero uniformly subsonic potential flows around bodies with three or more protruding corners.

Velocity cannot be globally bounded in incompressible flows.

Extends previous results to piecewise analytic boundaries and general equations of state.

Abstract

We prove that there are no nonzero uniformly subsonic potential flows around bodies with three or more protruding corners, for piecewise analytic boundary and for equation of state a $\gamma$-law with $\gamma>1$. This generalizes an earlier result limited to the low-Mach limit for nondegenerate polygons. For incompressible flows we show the velocity cannot be globally bounded.