Vortex flow around a circular cylinder above a plane

TL;DR

This paper analyzes vortex flow around a circular cylinder above a plane wall, deriving the complex potential using modern complex analysis techniques and illustrating the resulting streamline patterns.

Contribution

It introduces a novel complex analysis approach to model vortex flow around a cylinder above a plane, revealing new stationary vortex behaviors.

Findings

Stationary vortex forms in front of the cylinder

Complex potential derived for vortex in uniform stream

Streamline patterns illustrated for the flow

Abstract

The study of vortex flows in the vicinity of multiple solid obstacles is of considerable theoretical interest and practical importance. In particular, the case of flows past a circular cylinder placed above a plane wall has attracted a lot of attention recently. In this case, a stationary vortex is formed in front of the cylinder, in contradistinction to the usual case without the plane where a vortex pair is observed behind the cylinder. In the present work, we apply modern complex analysis techniques to obtain the complex potential for the problem of one point-vortex placed in a uniform stream past a circular cylinder above a plane. A typical streamline pattern is also shown.