Abstract
A family of exact stationary solutions of the Euler equations is presented. They are the generalizations of the Moore-Saffman vortex to N confocal ellipses that are embedded in a uniform background strain field e and a uniform background vorticity field 2γ. The two-dimensional linear instability of double ellipses is studied following Love, Moore & Saffman and Polvani & Flierl. Two types of instability are found. The first is the Love-type instability of the inner ellipse, which destabilizes an elliptical vortex patch whose aspect ratio is greater than 3. The second is the Rayleigh-type instability that occurs for concentric vortex patches with non-monotonic vorticity distribution.
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