Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T18:23:09.016Z Has data issue: false hasContentIssue false

Stability of vortices in equilibrium with a cylinder

Published online by Cambridge University Press:  18 November 2005

ALAN R. ELCRAT
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA
BENGT FORNBERG
Affiliation:
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, USA
KENNETH G. MILLER
Affiliation:
Department of Mathematics, Wichita State University, Wichita, KS 67260, USA

Abstract

The stability of steady inviscid vortex pairs in equilibrium with a circular cylinder is studied by discretizing equations derived from contour dynamics. There are two families of vortices, one with a pair of counter-rotating vortices standing behind the cylinder, which may be thought of as desingularizing the Föppl point vortices, and the other with the vortices standing directly above and below the cylinder. Vortices in the first family are found to be neutrally stable with respect to symmetric perturbations. When asymmetric perturbations are included, there is a single unstable mode and a single asymptotically stable mode. Vortices above and below the cylinder have two modes of instability, one symmetric and the other asymmetric, and likewise two asymptotically stable modes.

Type
Papers
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)