On rotating doubly connected vortices

Taoufik Hmidi; Joan Mateu; Joan Verdera

doi:10.1016/j.jde.2014.10.021

On rotating doubly connected vortices

Taoufik Hmidi, Joan Mateu, Joan Verdera

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface must be a confocal ellipse. We then discuss some relations, first found by Flierl and Polvani, between the parameters of the ellipses, the velocity of rotation and the magnitude of the vorticity in the domain enclosed by the inner ellipse.

Original language	English (US)
Pages (from-to)	1395-1429
Number of pages	35
Journal	Journal of Differential Equations
Volume	258
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2014.10.021
State	Published - Feb 15 2015

Keywords

2D incompressible Euler equations
Inverse problems
Potential theory
Rotating patches

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2014.10.021

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abstract = "In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface must be a confocal ellipse. We then discuss some relations, first found by Flierl and Polvani, between the parameters of the ellipses, the velocity of rotation and the magnitude of the vorticity in the domain enclosed by the inner ellipse.",

keywords = "2D incompressible Euler equations, Inverse problems, Potential theory, Rotating patches",

author = "Taoufik Hmidi and Joan Mateu and Joan Verdera",

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AU - Mateu, Joan

AU - Verdera, Joan

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AB - In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface must be a confocal ellipse. We then discuss some relations, first found by Flierl and Polvani, between the parameters of the ellipses, the velocity of rotation and the magnitude of the vorticity in the domain enclosed by the inner ellipse.

KW - 2D incompressible Euler equations

KW - Inverse problems

KW - Potential theory

KW - Rotating patches

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JF - Journal of Differential Equations

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ER -

On rotating doubly connected vortices

Abstract

Keywords

ASJC Scopus subject areas

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