Hexagonal 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 t...

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Bibliographic Details
Main Author: Brandolese, Lorenzo
Other Authors: Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Institut Camille Jordan Villeurbanne (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet Saint-Étienne (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Format: Report
Language:English
Published: HAL CCSD 2021
Subjects:
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
North Pole
Online Access:https://hal.archives-ouvertes.fr/hal-03125332
https://hal.archives-ouvertes.fr/hal-03125332/document
https://hal.archives-ouvertes.fr/hal-03125332/file/hexagonal-structure.pdf
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 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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