On the symmetry of self-organized structures in two-dimensional turbulence

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Abstract
We report a systematic investigation of equilibrium states predicted by the statistical theory of vortex patches in a square box, in a channel, and in a square with doubly periodic boundary conditions. The study is limited to initial conditions containing negative and positive vortex patches with equal strength and area. It is demonstrated that the symmetry between positive and negative vorticity is, in general, broken by the self‐organized states. Direct numerical simulations support the predictions of the vortex patch statistics, but agree with point vortex statistics only in the limiting case of small area vortex patches.