Document | Fichier |
---|---|
Fichier pdf chargé le 17/07/2015 à 12:22:20 Accès libre (version éditeur) | fichier |
Titre | A geometric interpretation of coherent structures in Navier–Stokes flows |
Type de publication | Article de revue |
Auteur | Roulstone, Ian, Banos, Bertrand, Gibbon, J. D, Roubtsov, Vladimir |
Pays | Royaume-Uni |
Editeur | Royal Society |
Ville | London |
Type | Article scientifique dans une revue à comité de lecture |
Année | 2009 |
Langue | Anglais |
Date | 2009/08/07 |
Numéro | 2107 |
Pagination | 2015 - 2021 |
Volume | 465 |
Titre de la revue | Proceedings. Mathematical, physical and engineering sciences |
ISSN | 1471-2946 |
Mots-clés | almost-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 notice | http://okina.univ-angers.fr/publications/ua191 |
DOI | 10.1098/rspa.2008.0483 |
Lien vers le document |