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Interaction of a Vortex Induced by a Rotating Cylinder with a Plane

Part of: Rotating fluids Incompressible viscous fluids

Published online by Cambridge University Press:  06 July 2017

Daozhi Han ,
Yifeng Hou  and
Roger Temam
Daozhi Han*
Affiliation:
Department of Mathematics & Institute for Scientific Computing and Applied Mathematics, Indiana University at Bloomington, 47405, USA
Yifeng Hou*
Affiliation:
Department of Mathematics & Institute for Scientific Computing and Applied Mathematics, Indiana University at Bloomington, 47405, USA
Roger Temam*
Affiliation:
Department of Mathematics & Institute for Scientific Computing and Applied Mathematics, Indiana University at Bloomington, 47405, USA
*
*Corresponding author. Email addresses:djhan@iu.edu (D. Han), houyifeng1005@hotmail.com (Y. Hou) temam@indiana.edu (R. Temam)
*Corresponding author. Email addresses:djhan@iu.edu (D. Han), houyifeng1005@hotmail.com (Y. Hou) temam@indiana.edu (R. Temam)
*Corresponding author. Email addresses:djhan@iu.edu (D. Han), houyifeng1005@hotmail.com (Y. Hou) temam@indiana.edu (R. Temam)
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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.

Keywords

Tornadoswirling vortexNavier-Stokesaxisymmetric flowboundary layer

MSC classification

Secondary: 76U05: Rotating fluids 76D03: Existence, uniqueness, and regularity theory 76D17: Viscous vortex flows 65Z05: Applications to physics
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 599 - 619
Copyright
Copyright © Global-Science Press 2017 

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