A geometric interpretation of coherent structures in Navier–Stokes flows

DocumentFichier
Fichier pdf chargé le 17/07/2015 à 12:22:20
Accès libre
(version éditeur)
fichier
TitreA geometric interpretation of coherent structures in Navier–Stokes flows
Type de publicationArticle de revue
AuteurRoulstone, Ian, Banos, Bertrand, Gibbon, J. D, Roubtsov, Vladimir
PaysRoyaume-Uni
EditeurRoyal Society
VilleLondon
TypeArticle scientifique dans une revue à comité de lecture
Année2009
LangueAnglais
Date2009/08/07
Numéro2107
Pagination2015 - 2021
Volume465
Titre de la revueProceedings. Mathematical, physical and engineering sciences
ISSN1471-2946
Mots-clésalmost-complex, Navier–Stokes, three-forms, turbulence
Résumé en anglais

The pressure in the incompressible three-dimensional Navier–Stokes and Euler equations is governed by Poisson's equation: this equation is studied using the geometry of three-forms in six dimensions. By studying the linear algebra of the vector space of three-forms Λ3W* where W is a six-dimensional real vector space, we relate the characterization of non-degenerate elements of Λ3W* to the sign of the Laplacian of the pressure—and hence to the balance between the vorticity and the rate of strain. When the Laplacian of the pressure, Δp, satisfies Δp>0, the three-form associated with Poisson's equation is the real part of a decomposable complex form and an almost-complex structure can be identified. When Δp<0, a real decomposable structure is identified. These results are discussed in the context of coherent structures in turbulence.

URL de la noticehttp://okina.univ-angers.fr/publications/ua191
DOI10.1098/rspa.2008.0483
Lien vers le document

http://dx.doi.org/10.1098/rspa.2008.0483