Vortex flow around a circular cylinder above a plane

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.