Geometric structures naturally appear in fluid motions. One of the best known examples is Saturns Hexagon, the huge cloud pattern at the level of Saturns north pole, remarkable both for the regularity of its shape and its stability during the past decades. In this paper we will address the spontaneous formation of hexagonal structures in planar viscous flows, in the classical setting of Lerays solutions of the Navier-Stokes equations. Our analysis also makes evidence of the isotropic character of the energy density of the fluid for sufficently localized 2D flows in the far field: it implies, in particular, that fluid particles of such flows are nowhere at rest at large distances.
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