  Geometric structures naturally appear in fluid motions. One of the best known
examples is Saturn's Hexagon, the huge cloud pattern at the level of Saturn's
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 Leray's 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.
