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The Sadovskii vortex in strain

Published online by Cambridge University Press:  21 July 2017

Daniel V. Freilich  and
Stefan G. Llewellyn Smith Open the ORCID record for Stefan G. Llewellyn Smith [Opens in a new window]
Daniel V. Freilich
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Stefan G. Llewellyn Smith*
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
*
†Email address for correspondence: [email protected]
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Abstract

The point vortex is the simplest model of a two-dimensional vortex with non-zero circulation. The limitations introduced by its lack of core structure have been remedied by using desingularizations such as vortex patches and vortex sheets. We investigate steady states of the Sadovskii vortex in strain, a canonical model for a vortex in a general flow. The Sadovskii vortex is a uniform patch of vorticity surrounded by a vortex sheet. We recover previously known limiting cases of the vortex patch and hollow vortex, and examine the bifurcations away from these families. The result is a solution manifold spanned by two parameters. The addition of the vortex sheet to the vortex patch solutions immediately leads to splits in the solution manifold at certain bifurcation points. The more circular elliptical family remains attached to the family with a single pinch-off, and this family extends all the way to the simpler solution branch for the pure vortex sheet solutions. More elongated families below this one also split at bifurcation points, but these families do not exist in the vortex sheet limit.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 479 - 501
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Copyright
© 2017 Cambridge University Press 

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