Inertial organization of a two-dimensional turbulent vortex street

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Abstract
The formation of organized structures resulting from the evolution of two parallel opposite vortex sheets in a two-dimensional perfect fluid is studied, employing an equilibrium statistical theory. The system is confined in a channel in which periodic solutions of the statistical equilibrium equations are considered. It is found that the statistical equilibrium state of maximum entropy is a staggered arrangement of alternating vortex patches—the turbulent counterpart to the von-Kármán vortex street. However, these vortices spread over the whole width of the channel and the pattern with the maximum allowed wavelength is always preferred: the confinement by the boundary conditions is essential. The theoretical predictions are supported by direct numerical simulations of the two-dimensional Navier–Stokes equation at high Reynolds number.