Interaction of a vortex induced by a rotating cylinder with a plane

TL;DR

This paper investigates the interaction between a vortex generated by a rotating cylinder and a plane, using theoretical and numerical methods to reveal vortex behaviors like boundary layer pumping and two-celled vortices.

Contribution

It introduces new theoretical solutions and numerical evidence for vortex-plane interactions, including phenomena observed in tornadoes and line vortices.

Findings

Existence of weak solutions to swirling vortex models.

Numerical demonstration of boundary layer pumping.

Observation of two-celled vortex phenomena.

Abstract

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.