Geometric structures in 2D Navier-Stokes flows

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 spontan...

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Bibliographic Details
Main Author: Brandolese, Lorenzo
Format: Article in Journal/Newspaper
Language:unknown
Published: CIRM 2020
Subjects:
EDP
Online Access:https://dx.doi.org/10.24350/cirm.v.19678603
https://library.cirm-math.fr/Record.htm?record=19287695124910058779
Description
Summary: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 sufficiently localized 2D flows in the far field: it implies, in particular, that fluid particles of such flows are nowhere at rest at large distances.