Consider a two-dimensional axisymmetric vortex with circulation Γ. Suppose that this vortex is isovortically deformed into an elliptical vortex. We show that the reduction in energy is ΔE=Γ2ln[(q+q1)/2]/(4π), where q2 is the ratio of the major to the minor axis of any particular elliptical vorticity contour. It is notable that ΔE is independent of the details of vorticity profile of the axisymmetric vortex and, in particular, independent of its average radius. The implications of this result for the two-dimensional inverse cascade are briefly discussed.

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