  In this article,we study theoretically and numerically the interaction of a
vortex induced by a rotating cylinder with a perpendicular plane. We show the
existence of weak solutions to the swirling vortex models by using the Hopf
extension method, and by an elegant contradiction argument, respectively. We
demonstrate numerically that the model could produce phenomena of swirling
vortex including boundary layer pumping and two-celled vortex that are observed
in potential line vortex interacting with a plane and in a tornado.
