Hexagonal structures in 2D Navier-Stokes flows

Abstract

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.

References in corpus (5)

• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2
• Global stability of vortex solutions of the two-dimensional Navier-Stokes equation
• Deep rotating convection generates the polar hexagon on Saturn
• Fine properties of self-similar solutions of the Navier-Stokes equations
• Infinite Energy Solutions for Damped Navier-Stokes Equations in R2